The ability of magnetic annuli to produce various magnetization configurations make them attractive for magnetic memory applications. In this study, the authors present NiFe/CoFe/Cu/CoFe current-perpendicular-to-plane giant magnetoresistive rings with 600 nm outer diameter and 200 nm inner diameter. By directly injecting current, it is shown that single-step vortex-vortex magnetic switching occurs due to contributions from an Oersted field and spin transfer torque. Experimental evidence reveals the spin transfer torque can either assist or act against the Oersted field by as much as 30% depending on the chirality of the reference layer in the CPP-GMR ring. The total switching contributions of the spin torque and the Oersted field are quantified and the mechanisms contributing to the magnitude of each contribution are discussed.