Does anyone know if there are remote internships for students?
Is there a place that lists them in a single site?
You can search Angellist for remote and internships I think.
I'm not sure about a site dedicated to this, but as @aviaryan mentioned you can search on regular job boards and use the right filters.
Having said that, I would advise against doing a remote internship. The beauty of an internship is that you get a chance to work with more experienced people and see what it's like to work at a company. I think by doing this remotely you lose out on much of that.