Well… not exactly. Most viruses don’t cause cancer but there are a good number of viruses that do. HTLV-1 and 2 (human T lymphoyropic virus) is strongly associated with adult T cell lymphoma, for example. And probably the most classic example of autoimmune disease -> viral infection -> cancer is Kaposi sarcoma. Patients with AIDS will get infected with HHV-8 (a type of herpes virus) and will then develop Kaposi’s sarcoma as a direct result.

They’re actually called oncoviruses, and are pretty well studied. Fascinating subject to research.