Is it permissible for a Kohen to marry a giyores (convert)?
A regular aged giyores, no.
There is a possibility,however, that perhaps this is due to the talmudic assumption that all non-Jews above the age of 3 are not virgins. The halacha might change with regard to a giyores who converted as an infant.
I think that possibility is raised in Yebamoth 60b but I do not know the final halacha.