Answer:
Although Tim Curry has been in the United States for several years, it is said he works via a work visa and has not relinquished his citizenship in Britian to become an American. Thus, he is not an American citizen and cannot vote in our country.
An intelligent guess would be that he is neither Republican or Democrat. Tim Curry keeps his dating life and his political views to himself, nevertheless; so, the answer is probably -- No, Tim Curry is not a Republican.