There are
no accredited universities currently offering a fully online PhD in Art History. A PhD program, especially in a field like art history which often involves primary source research (like examining original artwork or archives), typically requires significant in-person interaction, access to specialized libraries and archives, and close mentorship from professors. These elements are difficult, if not impossible, to replicate fully online.
While some universities may offer *some* online components within their traditional PhD programs in Art History, a completely online program at the doctoral level is extremely rare, if not nonexistent, in this field. You'd be far better off searching for programs with strong online components or distance learning options for certain courses, but expect a significant on-campus presence to be a requirement.