We report the first hybrid matter-photon implementation of verifiable blind quantum computing. We use a trapped-ion quantum server and a client-side photonic detection system networked via a fiber-optic quantum link. The availability of memory qubits and deterministic entangling gates enables interactive protocols without postselection-key requirements for any scalable blind server, which previous realizations could not provide. We quantify the privacy at ≲0.03 leaked classical bits per qubit. This experiment demonstrates a path to fully verified quantum computing in the cloud.