Can a F1 student go to an online school for graduate program?

I do not think so. For undergraduate you have to at least be enrolled in 9 credits of traditional classes. For online it should be something like 6/7 credits traditional, but as much as I know, you can not do it completely online. Before anyone writes something against this comment, I would rather say it myself, my answer is not authentic. Better check with the DSO of your school. It really depends on them.