Short answer
Only in the King James Version and in Bibles that follow the later Greek copies. These include the New King James Version and the World English Bible. The oldest Greek copies and all the early translations read "who" or "which", not "God": "He who was manifested (shown openly) in the flesh". Most modern Bibles follow them. In early Greek writing the two words look almost the same. They differ by a stroke or two of the pen. So a copyist's slip or choice could decide whether this verse calls Jesus God. The same letter says there is "one God, and one mediator between God and men, the man Christ Jesus". It also says no man has seen God (﷾) or can see Him. Many people saw Jesus, so the letter keeps God (﷾) and Jesus apart. Islam teaches that Jesus was a man and a messenger of God (﷾).
Full explanation
Why Christians cite the verse
In the King James Version, 1 Timothy 3:16 reads "God was manifest in the flesh". Manifest means shown openly. Christians have long treated this as one of the plainest statements that Jesus is God who became man.
“And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.”
What the oldest manuscripts say
Bruce Metzger, a twentieth-century scholar, wrote the leading guide to the Greek text of the New Testament. He finds that no Greek manuscript written in capital letters before the eighth or ninth century reads "God" here in its first hand. That means before any later corrector changed it. He finds that every ancient translation presupposes "who" or "which". He finds that no church writer before the late fourth century quotes "God". The Revised Version of 1881 and the American Standard Version of 1901 read "He who was manifested". Most modern Bibles follow them.
On 1 Timothy 3:16, concludes that "who" (hos) is the original reading. No uncial manuscript earlier than the eighth or ninth century supports "God" (theos) in its first hand; all the ancient translations presuppose "who" or "which"; and no church writer before the last third of the fourth century attests "God". "God" arose either by misreading the Greek letters or by deliberate change. He notes that "God" is the reading of the great majority of later Greek manuscripts (the Byzantine text).
The English Revised Version (1881) and the American Standard Version (1901), both public domain, follow the older manuscripts. Both begin the line "He who was manifested in the flesh" and do not have the word "God".
Most modern translations begin the line with "He" or "He who", not "God": the RSV and ESV ("He was manifested in the flesh"), the NRSV ("He was revealed in flesh"), the NASB ("He who was revealed in the flesh") and the NIV ("He appeared in a body" in 1984, "He appeared in the flesh" in 2011). The New King James Version keeps "God".
A stroke of the pen
Early Greek copies were written in capital letters, and scribes shortened sacred names. "God" was written ΘΣ with a line above it. "Who" was written ΟΣ. Add a small stroke inside the first letter and a line above, and "who" becomes "God". Scholars conclude that this is how the later reading arose, by accident or on purpose.
On 1 Timothy 3:16, concludes that "who" (hos) is the original reading. No uncial manuscript earlier than the eighth or ninth century supports "God" (theos) in its first hand; all the ancient translations presuppose "who" or "which"; and no church writer before the last third of the fourth century attests "God". "God" arose either by misreading the Greek letters or by deliberate change. He notes that "God" is the reading of the great majority of later Greek manuscripts (the Byzantine text).
Uses 1 Timothy 3:16 as an example of a scribal change: in Greek manuscripts "who" (ΟΣ) and the shortened form of "God" (ΘΣ) differ only by small strokes, and later copies came to read "God". Recounts the eighteenth-century scholar J. J. Wettstein's finding that Codex Alexandrinus originally read "who".
What the same letter says about God (﷾) and Jesus
1 Timothy speaks plainly elsewhere. It says there is one God, and one mediator between God (﷾) and men, "the man Christ Jesus". It says God (﷾) is immortal and invisible, and no man has seen Him or can see Him. Jesus was seen by many. In Mark, one of the New Testament Gospels, Jesus himself answers a man who called him good: none is good but one, that is, God (﷾).
“For there is one God, and one mediator between God and men, the man Christ Jesus;”
“Now unto the King eternal, immortal, invisible, the only wise God, be honour and glory for ever and ever. Amen.”
“Who only hath immortality, dwelling in the light which no man can approach unto; whom no man hath seen, nor can see: to whom be honour and power everlasting. Amen.”
“And Jesus said unto him, Why callest thou me good? there is none good but one, that is, God.”
What the Qur'an says about changed scripture
The Qur'an warns against those who write the Book with their own hands and then say it is from God (﷾). This verse, 1 Timothy 3:16, shows one place where the Bible's text changed as it was copied. By slip or by design, a single stroke put the word "God" into a verse that millions then read as God's (﷾) word. Some Christians still quote it as proof. Islam teaches that Jesus was a man and a messenger of God (﷾).
“Then woe to those who write the Book with their own hands, and then say:"This is from Allah," to traffic with it for miserable price!- Woe to them for what their hands do write, and for the gain they make thereby.”
Verse by verse
1 Timothy 3:16 — First Epistle to Timothy, chapter 3, verse 16
“And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.”
Cited for
"God was manifest in the flesh" is what the great majority of Greek manuscripts say, so it is the true text.
The response
Counting copies is not the test, because the earliest evidence points the other way. No manuscript in capital letters before the eighth or ninth century reads "God" in its first hand. Every ancient translation presupposes "who" or "which". No church writer quotes "God" before the late fourth century. A reading that many later copies repeat is still one reading.
Where it lands — The earliest evidence reads "who", so the verse does not call Jesus God.
1 Timothy 3:16 in the Revised Version (1881) and American Standard Version (1901)
The English Revised Version (1881) and the American Standard Version (1901), both public domain, follow the older manuscripts. Both begin the line "He who was manifested in the flesh" and do not have the word "God".
Cited for
Even with "He who", the verse still describes the incarnation of the Son.
The response
With "He who", the verse no longer names Jesus as God. The word "manifest" does not by itself mean he lived before. Compare 1 Peter 1:20, which says Christ "was foreordained before the foundation of the world, but was manifest in these last times". But 1 Timothy 3:16 itself speaks of one who appeared in the flesh, was seen, was preached and was taken up in glory. Elsewhere 1 Timothy calls him "the man Christ Jesus". It also says that no one has seen God (﷾).
Where it lands — Without the word "God" the verse is no proof text, and the letter itself separates God (﷾) from the man Christ Jesus.
Perspectives
King James defenders
"God was manifest in the flesh" is the true text. It is the reading of most surviving Greek manuscripts, and it states the incarnation plainly.
Most surviving Greek manuscripts of 1 Timothy read "God" at 3:16.
Rebuttal
Grant that most surviving Greek copies read "God". But counting copies is not the test. The earliest manuscripts and the ancient translations point to "who", and no church writer quotes "God" before the late fourth century.
The King James reading "God was manifest in the flesh" is the original and teaches that Jesus is God.
Rebuttal
The oldest evidence reads "who", so, on the evidence, the King James wording is not the original. The same letter says there is "one God, and one mediator between God and men, the man Christ Jesus". It also says no man has seen God (﷾), yet many saw Jesus.
The Islamic perspective
Jesus was a man and a messenger of God (﷾). The one verse in 1 Timothy that seems to call him God does so only in later copies. The letter's own teaching is one God, and the man Christ Jesus.
The earliest manuscripts and the ancient translations support "who", and no church writer before the late fourth century quotes "God".
The Revised Version, the American Standard Version and most modern Bibles read "He" or "He who", not "God".
In early Greek manuscripts the two readings differ by a stroke or two of the pen.
The same letter calls Jesus "the man Christ Jesus", a mediator between the one God (﷾) and men.
The same letter says God (﷾) is immortal and invisible, whom no man has seen or can see.
The Qur'an teaches that people wrote scripture with their own hands and called it God's (﷾) word.