This work presents a direct measurement of the Ru-96(p,gamma)Rh-97 cross section via a novel technique using a storage ring, which opens opportunities for reaction measurements on unstable nuclei. A proof-of-principle experiment was performed at the storage ring ESR at GSI in Darmstadt, where circulating Ru-96 ions interacted repeatedly with a hydrogen target. The Ru-96(p,gamma)Rh-97 cross section between 9 and 11 MeV has been determined using two independent normalization methods. As key ingredients in Hauser-Feshbach calculations, the gamma-ray strength function as well as the level density model can be pinned down with the measured (p,gamma) cross section. Furthermore, the proton optical potential can be optimized after the uncertainties from the gamma-ray strength function and the level density have been removed. As a result, a constrained Ru-96(p,gamma)Rh-97 reaction rate over a wide temperature range is recommended for p-process network calculations.