The State Department issues visas, and they are under the direction of the President. Without a visa, you can’t enter the country. So, all it takes is the stroke of a bureaucrat’s pen to say that a certain person will never be issued a visa, for whatever reason.
Not saying it’s right, just saying that’s the way it is.
The disturbing thing in this case is that the action seems to be simply because he annoyed Obama. I’ve never seen a president get so personally involved in exercising repressive powers over average citizens (or even non-citizens, now).