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.