Of course there is. Most people can't remember, because they think they're their own body, rather than a spiritual child of God.
Even John the Baptist could not remember being Elijah, but our Lord and Master told his disciples that Elijah had come but that no one recognized him. And the disciples knew he was speaking of John the Baptist. That's reincarnation.
Why would reincarnation exist?
Genesis 1:26 tells us that we were created in God's image. Just as Adam and Eve gave birth to baby humans, God gave birth to baby gods. Even Jesus said to his enemies, "ye are gods." And in our arrogance, we wanted to do things our own way. We consumed the product of physical dichotomies and lost our ability to see with the spirit. We each died on the day we ate of the forbidden fruit.
And later, God created Homo sapiens so that we may find our way out of the darkness. God wants all of His children back. Wouldn't the heavenly Father want to give His children every opportunity to awaken? Each reincarnation is another opportunity. Each incarnation is another chance for the potter to mold the clay into something useful.
And what did Christ mean when he said that he that lives by the sword shall die by the sword? Do all criminals die of the things they perpetrated? Not in their current life. Some die of old age, sleeping in their villas paid for by the blood of others. So, was Christ lying? Of course not! The only opportunity for karma to reap its full reward is in the next incarnation.
For the hardened heart of one lifetime, the next is an opportunity to have that heart softened and the door opened. Not everyone opens that door, but there's always next lifetime, right?
But why not this lifetime! The true self, within, must awaken.