There is no a final answer and the answer depends on many factors, including, but not limited to, the stage of the damage to the liver and whether the person is co-infected with the HIV virus. Two main specialty physicians, with the best knowledge needed to treat patients infected with Hep C, are hepatologists (liver doctors) and gastroenterologists (abdominal doctors). The first one is consider a sub-specialty of the second one.
Many patients co-infected with HIV may also be already receiving medical treatment from an infectious disease specialist. Usually a team of clinicians decides the protocol of medication treatment for such co-infected patients depending on their particular situation.