Short answer

Not in its hymns. Its funeral hymns send the dead to Yama (ruler of the dead) and the Fathers (the spirits of the ancestors), "in highest heaven". There they meet the merit of their deeds. None sends anyone back to be born again. Rebirth on earth is taught in the Upanishads, the Veda's last part. There a king tells a Brahmin (of the priest class) that this knowledge "did not go to any Brâhmana before you". It had belonged to the Kshatriyas, the warrior class, not to the priests who kept the hymns. The Upanishads and the Gita made the Fathers' heaven a stop on the way back to birth. The hymns' picture is nearer the Qur'an's: one life, then the dead meet their deeds, with no return. The verses cited for rebirth are answered below. Islam teaches that one life, and calls you to live it for God (﷾).

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