It is True, the word reincarnation does not appear in the Bible. However, there are a couple of references that strongly indicate reincarnation. One pretty clear example is from an interaction Jesus had with his disciples that indicated reincarnation was an accepted belief by Jesus and the disciples.
When Jesus saw a man that was blind from birth his disciples asked him who sinned that the man should be born blind, the man himself or his parents. (John 9:1) The disciples would not ask this question had they not known about the law of reincarnation. And Jesus did not rebuke them for the question. They were fully aware that it was entirely possible that the man could be blind because of sins committed in his previous life because there would be no other time that he would have committed them since he was blind from birth.
If the idea of the man being born blind from birth because of sins in a past life was incorrect, Jesus would have corrected the disciples. One of many examples where he did correct them is when they called him good master, “Good master, what shall I do to inherit eternal life?” Jesus did not even answer this question but rather challenged them on their idolatry of the human person saying, “Why callest thou me good? There is none good but God.” (Matthew 19:17). So we have good reason to believe that Jesus would have corrected the disciples if they were speaking incorrect concepts.
Regarding the blind man and the disciples’ question, Jesus did answer them. He said that neither had the man or his parents sinned, but that the man was born blind so that works of God should be made manifest in him.
This is also another teaching point for us. It tells us that it is possible that we might have a burden of an infirmity because we may have chosen ourselves to bear some karma for a loved one or that of the planet, or bearing a burden so that God could glorify himself within us through the healing process. We don’t always know what is behind our conditions in life.
Another clear example in the Bible of reincarnation was when Jesus said about John the Baptist, “And if ye will receive it, this is Elias, which was for to come. He that hath ears to hear, let him hear.” (Matthew 11:14). So if we have ears to hear, we will hear.
Keep in mind that there were many texts circulating within the Christian community in the first two centuries. Some were decided to be genuine and others not by church leaders. In 367 AD, the church father Athanasius chose the complete listing of the 66 books belonging to the canon of the church, which excluded a number of books.
In 1945, ancient writings were discovered that revealed information about the Gnostics, one of the early sects of Christianity and their beliefs in reincarnation. They claimed to have knowledge of Jesus’ secret teachings handed down to them by the apostles. The Gnostics were ultimately destroyed by the Roman Orthodox church because they were branded heretical. Their writings, which included some of the books that were eliminated from the final Bible canon, were destroyed and their followers burned at the stake.
Burning them at the stake? Do you think that someone had a vested interest in keeping the understanding of reincarnation out of the bible?
Then there was Origin of Alexandria who in the second century was one of the most distinguished theologians for the early church. His writings included teachings of Jesus on reincarnation and the heavenly hierarchy. His books were widely used for more than a century but at the same time were criticized. By the sixth century, his writings were declared to be heresy and condemned. His writings were destroyed with only a few remaining today.
So we cannot claim authoritatively that reincarnation is not in the Bible. And in light of the 1945 discovery of the Nag Hammadi texts in Egypt, we cannot say authoritatively that Jesus did not teach or believe reincarnation himself. And not to mention that the majority of the population of earth believes in reincarnation.
In addition, there have been some amazing of children remembering a past life. One of the most impressive and documented cases is that of James Leininger. Check it out here.
Again, we cannot claim authoritatively that reincarnation is not, or was not, in the Bible.
Remember, you are divine. You were created for a purpose. And that purpose is unique. While here, you are meant to externalize and develop your unique divine qualities and then return back to God.