Hi Barb,
It's certainly used for teachers, as you know. It's also used as in I've applied to the Faculty of Modern History at XYZ University. In a sense, that's like talking about a 'department'.
Hence, I think that when teachers speak more carefully, they might often say I'm a faculty member or I'm on/in the faculty. Students might also be in the Faculty of Modern History, but I don't think they speak of being faculty members.
I also think such defintions/usage are likely to vary between countries.
Best wishes , Clive