Technically no, since the reservation has to be in the name of the person picking up the rental and that person is supposed to be a member, but it depends on whether the agent at the counter asks for proof of membership (they usually don't). You could also ask your parents to add you as a family member to their membership and then you'd get your own card and also have all the benefits of AAA membership yourself. This is typically about $30 per year, and sometimes it's even less for the first year, so worth asking.