This is answered on their admissions pages for each course - did you actually read the requirements?
The history of art masters at Oxford just requires a good first degree in a humanities or social science. Archaeology would be perfectly suitable (perhaps especially so for some topics). They specifically state: "Most successful applicants have a degree in a humanities subject such as history of art, history, English, modern languages, Classics, theology, philosophy, archaeology or anthropology. Graduates in fine art who have excellent research and writing skills will also be considered. Applicants with social science and sometimes even science degrees have also been admitted provided they can make a persuasive application that attests to their interest in the visual arts, broadly defined, and demonstrates excellent preparation for the course’s research and writing demands. A degree in history of art is not a requirement and approximately half of each cohort will have completed an undergraduate degree in another subject." - emphasis mine.
The MSt History at Oxford requires a strong first degree in a relevant humanities or social science course, and notes that: "applicants are not expected to have a previous degree in history, but are expected to have experience of working historically. You will need to ensure that you link your proposed dissertation topic with your previous expertise, explain why you want to switch to study history, and show that you have already done some background research.". Since an archaeology degree will necessarily involve working historically if you've done any historical archaeology, provided you can provide a cogent reason for wanting to do history rather than archaeology there is no issue.
You really will need to be able to do this basic research if you expect to cope with a demanding masters course anywhere though. This is literal 30 seconds of googling level research.