Those that refer to the Bible as truth, should believe that reincarnation is real and sometimes happens. Not everyone is reincarnated, but some spirits do request from God another opportunity to earn merits in this life. Here are two examples:

John the Bapist ~ was the reincarnation of Elijah, also called Elias. Here is what Jesus said of him:

For all the prophets and the law prophesied until John. And if ye will receive it, this is Elias, which was for to come. He that hath ears to hear, let him hear. Matthew 11:13-15 KJV

So the Lord said so himself that John was Elias (in the Old Testament: Elijah). That one example alone should be enough to convince Bible-believers that reincarnation is real and is sometimes allowed by God.

Man born blind ~ was a reincarnated man, having lived a previous life, but the wording in the Bible is subtle, so think about the wording.

And as Jesus passed by, he saw a man which was blind from his birth. And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind? Jesus answered, Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him. John 9:1-3 KJV

Why would the disciples ask the Lord if the man was born blind because of his own sin? How could the man sin before his birth? They knew of reincarnation and wondered if the man in his previous life had sinned, and so as a way to atone for that sin was given another life with the handicap of blindness. Jesus did not rebuke his disciples for thinking the man was reincarnated, but implied that this man agreed to come into the world again, blind, to show the glory of God. And that man was healed with a personal visit from the Lord Jesus Christ! The man came into the world again to showcase one of God's miracles, and to deliver a famous verse that we should all say, who now believe the truth....

I was blind, but now I see!