In his On First Principles, he seems to propose a theory of preexistent souls that are incarnated because of a sort of neglect of the God above them. (This was likely something his teacher Ammonius Saccas taught, as we see a similar idea in Plotinus, another one of his students.) But that’s not re-incarnation, an already incarnated soul migrating into another body. There are, however, some passages in that book that suggest such a doctrine, but I don’t believe they’re entirely conclusive (it’s been a while since I read it). But Origen is quite clear that, in On First Principles, he’s engaging in speculative theology, and that nothing he says there should be taken as his considered view of things or official doctrine.
https://youtu.be/CmDW2Y5VWAo