Reincarnation is a topic about which the Bible is fairly quiet.
There is a text—Hebrews 9:27—that says, “It is appointed unto men once to die, but after this the judgment.”
But is this a comment on reincarnation? Or is it, rather, a conventional statement? Any particular man—John W. Smith—is born but once, and dies but once. This we all know. Whether his soul then enters another lifetime is another matter.
The Vedic literature says that when any man dies, the acts of his life are weighed—he is judged. And then he takes his next birth accordingly. Is this in conflict with the text? You decide.
But before you do, please take into account the entire text:
And as it is appointed unto men once to die, but after this the judgment: So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation. (Hebrews 9:27-28)
The focus here is not on the question of whether the soul undergoes transmigration. Rather, a common example is being given by which to better understand the divine sacrifice offered by Christ.
There seems little reason to suppose that the use of this example rules out reincarnation.
Sometimes a text from Matthew (17:9-12) is offered as evidence of reincarnation. There Jesus tells his disciples that Elias had come again as John the Baptist. This text, however, does little to support the doctrine of reincarnation. It fits better with the Vedic concept of avatara—the doctrine that God, God’s son, or one of God’s messengers from the spiritual world may, by spiritual power, appear through birth in the world for the upliftment of the fallen souls. (Christians may find that this Vedic doctrine resonates with their own beliefs, or even offers a way to greater understanding—but that is another matter.)
A more relevant text appears in John (9:1-2):
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?
The idea that the man was born blind due to the sins of his parents is easily intelligible: because of their own sins, the parents had a son who was blind.
But how are we to understand that a man could have been born blind due to sins of his own? Clearly, the man must have lived before. Of course, one could say that the man must have sinned in the womb. But this is a very strange explanation. What sin could the man have done there—crossed his legs wrong? Would the disciples have even entertained such ideas? Surely the alternative they are asking about is the possibility that the man had sinned in a previous life, an alternative that fit with a doctrine taught for centuries before Christ and undoubtedly still current while he was on earth—the doctrine of reincarnation.
And how does Jesus answer? Does he upbraid the disciples for their foolishness? Does he condemn them for bringing up a worthless or repugnant idea? Does he tell them in no uncertain terms that reincarnation is a mistake, a wrong teaching, an error?
Surely, here was an ideal opportunity to do so. But Jesus doesn’t.
Instead, in the next verse, he answers, “Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him.”
In other words, this is a special case, a setup. The man has been born blind so that Jesus may show a miracle, as he does a few verses later.
And so Jesus comments on neither of the offered alternatives—the sins of the parents nor the past sins of the man himself—but simply puts forward a different story.
As we see, reincarnation is an idea that Lord Jesus declines the opportunity to refute.