In the City of God, St. Augustine writes:
Mirabilius autem quiddam Marcus Varro ponit in libris, quos conscripsit de gente populi Romani, cuius putavi verba ipsa ponenda. “Genethliaci quidam scripserunt, inquit, esse in renascendis hominibus quam appellant παλιγγενεσίαν Graeci; hac scripserunt confici in annis numero quadringentis quadraginta ut idem corpus et eadem anima quae fuerint coniuncta in homine aliquando eadem rursus redeant in coniunctionem."
(Moreover, in the books which he wrote On the Race of the Roman People Marcus Varro sets down a more marvellous thing. I think his words should be quoted: “Certain astrologers have written that there is a rebirth of men which the Greeks call palingenesia, by which in four hundred forty years the same body and soul which were once joined in a man come back to be joined once more.”)
(Translated by William Green)
So, the term used is renascor (rebirth). There is also the word regeneratio which is found in biblical contexts, although I am not certain being born again as in the New Testament (or in the above from Augustine) qualifies as reincarnation because reincarnation I think implies being born again in a different body, not the same body.