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Hybrid quantum systems involving cold atoms and microwave resonators can enable cavitymediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave to optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric dipole transitions. Here we report on the realization of coherent coupling of a Rydberg transition of ultracold atoms trapped on an integrated superconducting atom chip to the microwave field of an on-chip coplanar waveguide resonator. We observe and characterize the cavity driven Rabi oscillations between a pair of Rydberg states of atoms in an inhomogeneous electric field near the chip surface. Our studies demonstrate the feasibility, but also reveal the challenges, of coherent state manipulation of Rydberg atoms interacting with superconducting circuits.