This question is about the famous Egyptologist. I read that he was educated at Eton and Trinity College, but cannot find information about his time at Cambridge - in particular what degree he obtained.
According to Brian Fagan's Lord and Pharaoh: Carnarvon and the Search for Tutankhamun, p. 55, he was "sent down for academic reasons after a year." So he did not obtain any kind of degree. The book doesn't indicate what he studied.
This seems consistent with his earlier studies at Eton, which were quite unsuccessful; Fagan speculates that he may have had some kind of learning disability.