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Individually addressed Er^{3+} ions in solid-state hosts are promising resources for quantum repeaters, because of their direct emission in the telecom band and their compatibility with silicon photonic devices. While the Er^{3+} electron spin provides a spin-photon interface, ancilla nuclear spins could enable multiqubit registers with longer storage times. In this work, we demonstrate coherent coupling between the electron spin of a single Er^{3+} ion and a single I=1/2 nuclear spin in the solid-state host crystal, which is a fortuitously located proton (^{1}H). We control the nuclear spin using dynamical-decoupling sequences applied to the electron spin, implementing one- and two-qubit gate operations. Crucially, the nuclear spin coherence time exceeds the electron coherence time by several orders of magnitude, because of its smaller magnetic moment. These results provide a path toward combining long-lived nuclear spin quantum registers with telecom-wavelength emitters for long-distance quantum repeaters.