We demonstrate optical coupling between a single tin-vacancy (SnV) center in diamond and a free-standing photonic crystal nanobeam cavity. The cavities are fabricated using quasi-isotropic etching and feature experimentally measured quality factors as high as ∼11 000. We investigate the dependence of a single SnV center's emission by controlling the cavity wavelength using a laser-induced gas desorption technique. Under resonance conditions, we observe an intensity enhancement of the SnV emission by a factor of 12 and a 16-fold reduction of the SnV lifetime. Based on the large enhancement of the SnV emission rate inside the cavity, we estimate the Purcell factor for the SnV zero-phonon line to be 37 and the coupling efficiency of the SnV center to the cavity, the β factor, to be 95%. Our work paves the way for the realization of quantum photonic devices and systems based on efficient photonic interfaces using the SnV color center in diamond.