Yes, if you type terms like 'fine art graphic design degree online' in a search engine you will get a page of results. If you want to be more specific, you could try putting just the words 'fine art online degree' and then 'graphic design online degree' to get two separate searches.
Some universities offer online versions of their mainstream courses, and there are also institutions that offer online courses only. An example of these is the Interactive Design Institute, which specialises in a variety of art related subjects going from basic City & Guilds and foundation courses to honours degrees.
With so many organizations and so much choice, the quality is bound to vary widely, as is the cost. Before enrolling on a course it would be a very good idea to have a talk with a careers advisor or contact a local college to ask for guidance. Good luck.