I think that both answers are technically okay for communication, but the answer is 'have' because although your subject (the girl) is singular, graduating classes are big and she is one in a pool of students who have graduated from the college. It's not so much about the singular subject, but about the group that she represents (all the girls who have graduated), if that makes any sense.

You hear people using both of them: The singular form referring to “one” or the plural form referring to “the girls who...” however I personally use the plural form because that is what the relative clause refers to.

I wouldn't worry too much as you will hear both versions (has and have) in day to day conversation. I would use 'has' myself because I have the individual (she) in my mind. Grammatically, 'have' is probably the 'correct' answer as the subject is the 'group of cleverest girls' and because it's plural, 'have' is required to agree with it.