There are a few things that you could major in. History or anthropology would be the most obvious choices. All colleges offer degrees in history and most would offer anthropology as well. As to what you could do with that degree after graduation would depend on what type of work interests you. You could teach (high school, college) or you could do field work actually digging up, catalogueing, and interpreting ancient artifacts. You would also have to gain a solid knowledge of some foreign language, especially Greek, Latin, German (much of past historical/anthropological academic work is in German), or the language of the civilization you are interested in studying.
