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We present two novel matter-wave Sagnac interferometers based on ring-shaped time-averaged adiabatic potentials, where the atoms are put into a superposition of two different spin states and manipulated independently using elliptically polarized rf-fields. In the first interferometer the atoms are accelerated by spin-state-dependent forces and then travel around the ring in a matter-wave guide. In the second one the atoms are fully trapped during the entire interferometric sequence and are moved around the ring in two spin-state-dependent ‘buckets’. Corrections to the ideal Sagnac phase are investigated for both cases. We experimentally demonstrate the key atom-optical elements of the interferometer such as the independent manipulation of two different spin states in the ring-shaped potentials under identical experimental conditions.