Carter Braxton was an Episcopalian.
From: Robert G. Ferris (editor), Signers of the Declaration: Historic Places Commemorating the Signing of the Declaration of Independence, published by the United States Department of the Interior, National Park Service: Washington, D.C. (revised edition 1975), page 41-42:
Carter Braxton, an aristocratic planter and probably the most conservative of the seven Virginia signers, originally opposed independence but later changed his mind and signed the Declaration. His tour in the Continental Congress lasted less than a year, but he held State office for most of his life. His two wives bore him 18 children, more than any other signer fathered.
Note that numerous sources and authoritative references have been consulted in order to ascertain the religious affiliation of the American Founding Fathers. Note that the excerpts and references mentioned on this page are not the only references used in order to identify this person's religious affiliation.