As Chris and Micheal have said, the correct answer is "is." However, many native speakers will say "are" in a sentence like this, because they get confused by the plural word "students," which seems to be the subject since it comes right before the verb. If you say "are," most people will not notice the mistake. In writing, though, it would be best to use the correct form, "is."

The correct answer, grammatically, is "is." "One of my students" is a singular subject.

Hello. I am a native speaker and read a lot, so I can tell you what sounds correct, but I am not a trained teacher. I had to think about this. "anyone" would seem to mean a singular subject. The confusing part is that "Students" is directly before the verb. In spoken conversation, I wouldn't notice which one a person said to me. For example, I use "is" with anyone a lot.: "Is anyone coming to dinner with us?" "Anyone is welcome to eat." Here is an article that will help make it even more confusing (haha): https://www.thoughtco.com/anyone-and-any-one-1692713