Although the bible doesn’t teach reincarnation in the way that the Hindu scriptures teach it, the bible suggests that God has power of the souls of those who die, and may reincarnate it if He so pleases.
There are several pieces of evidence in the bible which suggests this. One such is the story of John the Baptist. The bible makes it clear in the New Testament Book of Matthews that John the Baptist was a reincarnation of the prophet Elias.
While Jesus was talking about His imminent deliverance into the hands of men, His disciples questioned “but wasn’t it written that Elias was supposed to come first?” (Matthews 17: 10-13).
Jesus then told them that Elias has already come and gone. Matthews 17: 13 makes it clear that John the Baptist was a reincarnation of Elias.