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I don't know. But HPV and Herpes definitely can. Here's some more: https://www.cancer.org/cancer/cancer-causes/infectious-agent... It takes quite a long time to prove the link between a viral infection and a cancer that develops decades later, so it'll be a while before we know for sure.
I think that given the fact that we've been getting sick from corona-family viruses for years with no suspected link to cancers, this should be of relatively low concern, barring any specific information. There are other potential longer term side effects that at least seem to have some emerging data to back them up, which seem more concerning to me.
How would we even know? In order to tell if coronaviruses caused cancer, we'd need to be keeping track of which people had ever been infected with one of them and how many of them ended up with cancer, and we're not. It'd just fall into the background level of cancer incidence otherwise. Hell, we haven't even figured out if they're the main cause of Kawasaki disease yet, and that's a fairly spectacular and dangerous condition affecting children. There's some evidence that some common viruses in the family might be really deadly to elderly people, but that doesn't seem to have been researched much either. There's a lot we just don't know.