It all depends on where you live and what your individual club is offering. There are AAA clubs nationwide and each is run independently, so you are bound by what your local club offers. Annual membership fees vary significantly from club to club--usually the more you pay the more benefits you enjoy. I suggest that you call your local AAA office and inquire. It can't hurt.
(By the way, I work for AAA Auto Club South in Florida. And while I don't work in the membership department, I am not aware of any free or trial membership offers at this time. But for those of you living in Florida, Georgia, or Tennessee--our club's territory--it still wouldn't hurt to call a AAA office to check.)