Good article on Biblically-supported reincarnation here, though I came to the same conclusion separately:
ocoy.org
Many Bible quotes can be found within that support this concept. I won't spam the page up by listing them all redundantly when the article does a nice enough job. Here is one quote I feel is particularly ironclad:
Genesis 9:6
6 Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man.
This would not be possible without reincarnation. As you know, many murderers are imprisoned or evade capture and die of natural causes.
The common counterargument to Christian reincarnation is the idea of an eternal hell which is countered here:
Tobit 13:2
“For he doth scourge, and hath mercy: he leadeth down to hell, and bringeth up again: neither is there any that can avoid his hand.”
How can one come out of hell without another chance at life?
On moral grounds, I would reject the concept of eternal hell, as an all-loving God would not create a being to suffer for all eternity. In fact, the Bible says that God will go through great lengths to save everyone, not stopping until He has succeeded.
www.kingjamesbibleonline.org
4 What man of you, having an hundred sheep, if he lose one of them, doth not leave the ninety and nine in the wilderness, and go after that which is lost, until he find it?
Furthermore, the idea of a loving God throwing sinners into eternal hell isn't just either - it is a cop-out. If you have an argument with someone, you can't win the argument by silencing them, only by proving them wrong. Evil can't be defeated with violence, only by turning evil to good can it be defeated in a moral sense. Hence, turn the other cheek. The question of good and evil, I would go so far as to say, is the fundamental question of our universe. It is one of the first things written about in the Bible, in Genesis chapter 3. So did God create evil just to lock it away? Or is there in fact a higher purpose to it? My personal theory is that your soul retains memory of its past suffering, and after experiencing evil, becomes more compassionate. Across the cycles, a soul gradually rises in consciousness from a base and evil state to a good and holy state, through toiling and suffering.
Now here is where I am about to get really unorthodox: human souls can transmigrate into animal souls. This is why the Hebrews sacrificed lambs and goats. A Jew repents for his sins by killing HIMSELF in his next life. A penance cycle as a lamb destined for slaughter. Therefore, the spiritual timeline of the world is not the same as the material timeline. A soul can be born to live concurrently with its previous or subsequent incarnation.
Now, how can Jesus atone for the collective sins of all mankind? There is only one possible explanation. Jesus is the Son of Man. The spiritual son, IE. the reincarnation of Man. The sum total of all human incarnations with a fully awakened soul memory.
Matthew 25:40
And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.
Or in other words: all life in our universe really only has a single soul, which is inferior to God, but is in the process of purifying itself to return to God.
Philosophers have often grappled with the quesion: how can a loving God create a universe filled with so much evil? Well the answer to this is clear: it's a moral lesson. We think there is good and evil but we've really just been screwing ourselves over for thousands of years. Everything we do meets with exact justice because we suffer at our own hands and learn from it.
So whose moral education was this universe created for? The book of Job has the answer.
Job 1
8 And the LORD said unto Satan, Hast thou considered my servant Job, that there is none like him in the earth, a perfect and an upright man, one that feareth God, and escheweth evil?

May a Christian Believe in Reincarnation?
This brief study of reincarnation will be to determine if in good conscience a Christian may believe in reincarnation. You will be surprised!

Many Bible quotes can be found within that support this concept. I won't spam the page up by listing them all redundantly when the article does a nice enough job. Here is one quote I feel is particularly ironclad:
Genesis 9:6
6 Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man.
This would not be possible without reincarnation. As you know, many murderers are imprisoned or evade capture and die of natural causes.
The common counterargument to Christian reincarnation is the idea of an eternal hell which is countered here:
Tobit 13:2
“For he doth scourge, and hath mercy: he leadeth down to hell, and bringeth up again: neither is there any that can avoid his hand.”
How can one come out of hell without another chance at life?
On moral grounds, I would reject the concept of eternal hell, as an all-loving God would not create a being to suffer for all eternity. In fact, the Bible says that God will go through great lengths to save everyone, not stopping until He has succeeded.

Luke chapter 15 KJV (King James Version)
Luke chapter 15 KJV (King James Version)

Furthermore, the idea of a loving God throwing sinners into eternal hell isn't just either - it is a cop-out. If you have an argument with someone, you can't win the argument by silencing them, only by proving them wrong. Evil can't be defeated with violence, only by turning evil to good can it be defeated in a moral sense. Hence, turn the other cheek. The question of good and evil, I would go so far as to say, is the fundamental question of our universe. It is one of the first things written about in the Bible, in Genesis chapter 3. So did God create evil just to lock it away? Or is there in fact a higher purpose to it? My personal theory is that your soul retains memory of its past suffering, and after experiencing evil, becomes more compassionate. Across the cycles, a soul gradually rises in consciousness from a base and evil state to a good and holy state, through toiling and suffering.
Now here is where I am about to get really unorthodox: human souls can transmigrate into animal souls. This is why the Hebrews sacrificed lambs and goats. A Jew repents for his sins by killing HIMSELF in his next life. A penance cycle as a lamb destined for slaughter. Therefore, the spiritual timeline of the world is not the same as the material timeline. A soul can be born to live concurrently with its previous or subsequent incarnation.
Now, how can Jesus atone for the collective sins of all mankind? There is only one possible explanation. Jesus is the Son of Man. The spiritual son, IE. the reincarnation of Man. The sum total of all human incarnations with a fully awakened soul memory.
Matthew 25:40
And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.
Or in other words: all life in our universe really only has a single soul, which is inferior to God, but is in the process of purifying itself to return to God.
Philosophers have often grappled with the quesion: how can a loving God create a universe filled with so much evil? Well the answer to this is clear: it's a moral lesson. We think there is good and evil but we've really just been screwing ourselves over for thousands of years. Everything we do meets with exact justice because we suffer at our own hands and learn from it.
So whose moral education was this universe created for? The book of Job has the answer.
Job 1
8 And the LORD said unto Satan, Hast thou considered my servant Job, that there is none like him in the earth, a perfect and an upright man, one that feareth God, and escheweth evil?