Does he have to divorce his wife if she rejects Islam?

If
your wife is from among the People of the Book – Jewish or Christian
– then you do not have to divorce her; you can keep her and this is
permissible. But if your wife is a follower of another religion, or
has no religion at all, then the very fact of your being Muslim means
that you must be separated, because it is not permissible for a Muslim
to be married to a mushrikah; if he does that then he is a zaani (fornicator,
adulterer) and that is not a (valid) marriage.