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our school has a bad policy saying that all RA are work-study positions.
If you are not work study eligible, then you are out.

what about your school?

why would a professor break the rule and take you as his or her RA if you are not eligible?

Profs aren't going to break the rule because they can't. Your law school or university administration controls the money, not the prof. Unless the prof is willing to pay you out of his own pocket (highly unlikely) then you are stuck. If you don't like the rule, your only shot at recourse is to try to get your school's SBA to circulate a petition to students and profs. Even so, that probably won't do anything because work study is Federal money, and if the school doesn't have internal $ to spend towards research assistants they aren't going to change the rule.

Of course, you can always see about doing UNPAID RA work if you want. I wouldn't bother though.

the problem is that even if you are willing to do unpaid RA work, the prof will not likely take you..... right??

I have no idea, I didn't go to your law school. You'll have to ask. Why are you so hard up to RA for some prof? I promise you the work will be boring, plus it's nothing like real world legal experience, which is what you should be seeking out. Especially if you are willing to do unpaid work.