quantum processors with optical telecommunication channels. High-frequency gigahertz piezo-mechanics featuring low thermal excitations offers an ideal platform to mediate microwave-optical coupling. However, integrating nanophotonic and superconducting circuits at cryogenic temperatures to simultaneously achieve strong photon-phonon interactions remains a tremendous challenge. Here, we report the first demonstration of an integrated superconducting cavity piezo-optomechanical converter where 10-GHz phonons are resonantly coupled with photons in a superconducting microwave and a nanophotonic cavities at the same time. Benefited from the cavity-enhanced interactions, efficient bidirectional microwave-optical photon conversion is realized with an on-chip efficiency of 0.07% and an internal efficiency of 5.8%. The demonstrated superconducting piezo-optomechanical interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in hybrid quantum systems such as microwave-optical photon entanglement and quantum sensing.