Atomic magnetometry is one of the most sensitive ways to measure magnetic fields. We present a method for converting a naturally scalar atomic magnetometer into a vector magnetometer by exploiting the polarization dependence of hyperfine transitions in rubidium atoms. First, we fully determine the polarization ellipse of an applied microwave field using a self-calibrating method, i.e., a method in which the light-atom interaction provides everything required to know the field in an orthogonal laboratory frame. We then measure the direction of an applied static field using the polarization ellipse as a three-dimensional reference defined by Maxwell's equations. Although demonstrated with trapped atoms, this technique could be applied to atomic vapors, or a variety of atomlike systems.