If I'm a permanent resident, can I marry someone with a student visa?

Yes, you marry someone with an F1 visa. However, the immigration filing will not provide any authorization for them. They will need to maintain their status until the case is process (several years). However, the best option is to file for your US citizenship and then petition or upgrade the case.

You can certainly marry a person with a student visa but you are not able to confer any immediate immigration benefits upon that person.  IT currently takes about 2-3 years for a petition filed by a permanent resident on behalf of a spouse.  However, depending on when you are eligible to apply for US citizenship, once you are a US citizen, that petition time is significanly expedited.