Short answer
Not in the usual Western sense, but Islam has its own way for two people to come together, and it protects them both. Islam keeps sex for marriage, and it tells believers not even to come near it outside marriage. So it also closes the doors that lead there, such as a man and a woman being alone together. Men and women are both told to lower their gaze. But Islam does not ask anyone to marry a stranger. A man and a woman thinking of marriage may meet and talk, as long as they are not alone together, and the Prophet (ﷺ) told a man to go and look at the woman he meant to marry. No one may be married without their consent. And the Prophet (ﷺ) urged the young to marry when they could. Love is not the problem. Islam gives it a home in marriage, where the Qur'an says God (﷾) puts love and mercy between husband and wife.
Full explanation
Not even near
The Qur'an does not only forbid sex outside marriage. It says: "Nor come nigh to adultery: for it is a shameful (deed) and an evil, opening the road (to other evils)." So Islam closes the road as well as the end of it. The Prophet (ﷺ) said that no man should be alone with a woman unless a close relative of hers is there. And the Qur'an tells believing men, and then believing women, to lower their gaze and guard their modesty.
“Nor come nigh to adultery: for it is a shameful (deed) and an evil, opening the road (to other evils).”
Ibn Abbas reports that the Prophet (ﷺ) said that no man should be alone with a woman except in the presence of a mahram (a close relative she may not marry), and that no woman should travel except with a mahram.
“Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And Allah is well acquainted with all that they do.”
“And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! turn ye all together towards Allah, that ye may attain Bliss.”
No secret lovers
When the Qur'an speaks of marriage, it says a man should seek a wife in chastity, "not lewdness, nor secret intrigues". The Arabic speaks of taking secret companions. That is close to what people now call a girlfriend or boyfriend. The bond Islam allows between a man and a woman is open and known to their families, and it leads to marriage.
“This day are (all) things good and pure made lawful unto you. The food of the People of the Book is lawful unto you and yours is lawful unto them. (Lawful unto you in marriage) are (not only) chaste women who are believers, but chaste women among the People of the Book, revealed before your time,- when ye give them their due dowers, and desire chastity, not lewdness, nor secret intrigues if any one rejects faith, fruitless is his work, and in the Hereafter he will be in the ranks of those who have lost (all spiritual good).”
Getting to know each other
Islam does not ask people to marry blind. A man told the Prophet (ﷺ) that he had agreed to marry a woman. The Prophet (ﷺ) asked whether he had looked at her. When he said no, the Prophet (ﷺ) told him to go and look. So a man and a woman who are thinking of marriage may meet and talk, with family around them rather than alone. And no one may be married against their will. The Prophet (ﷺ) said a woman is not to be married without her consent.
Abu Hurayra reports that a man told the Prophet (ﷺ) he had agreed to marry a woman of the Ansar. The Prophet (ﷺ) asked whether he had looked at her. He said no, and the Prophet (ﷺ) told him to go and look at her.
Ibn Abbas reports that the Prophet (ﷺ) said that no man should be alone with a woman except in the presence of a mahram (a close relative she may not marry), and that no woman should travel except with a mahram.
Abu Huraira reports that the Prophet (ﷺ) said a woman who has been married before is not to be married again without being consulted, and a virgin is not to be married without her permission.
Marry, and do not wait too long
The Prophet (ﷺ) told the young men around him that whoever could afford to marry should marry, because marriage helps a person lower the gaze and stay chaste. Whoever could not, he said, should fast. Islam does not ask young people to fight their feelings for years. It asks families to make marriage easier, not harder.
Abdullah ibn Mas'ud reports that the Prophet (ﷺ) told the young men with him: whoever of you is able to marry should marry, because it helps him lower his gaze and guard his chastity; and whoever cannot should fast.
Love has a home
Islam does not treat love as a sin. The Qur'an calls marriage one of God's (﷾) signs: "He created for you mates from among yourselves, that ye may dwell in tranquillity with them, and He has put love and mercy between your (hearts)". What Islam forbids is not love, but taking what belongs to marriage without the commitment of marriage.
“And among His Signs is this, that He created for you mates from among yourselves, that ye may dwell in tranquillity with them, and He has put love and mercy between your (hearts): verily in that are Signs for those who reflect.”
Perspectives
You need to date to know someone
Many people say you cannot know whether you suit someone until you have dated them. Marrying without it, they say, is a gamble.
Without dating, people marry someone they do not really know.
Rebuttal
Islam does not forbid getting to know someone, only being alone together. A man and a woman may meet, talk and ask about each other, with their families involved. The Prophet (ﷺ) told a man to go and look at the woman before he married her. What Islam keeps for marriage is the closeness that belongs to it.
The Islamic perspective
Islam keeps sex for marriage, and it closes the doors that lead there, such as being alone together. A man and a woman thinking of marriage may get to know each other openly. No one may be married without their consent. Love has its home in marriage, where God (﷾) puts love and mercy between husband and wife.
The Qur'an forbids coming near to adultery.
The Prophet (ﷺ) said no man should be alone with a woman unless a close relative of hers is present.
The Prophet (ﷺ) told a man to look at the woman he meant to marry.
A woman is not to be married without her consent.
The Prophet (ﷺ) urged young people to marry when they could.