Charged particle acceleration via the shock drift mechanism at quasi-perpendicular shocks has generally been analyzed by assuming uniform, time-independent conditions at and near the shock. We present results from a model designed to study how the shock drift mechanism is modified when wave activity is included in the shock's upstream and downstream vicinities. The technique involves numerically following test particle trajectories in the wave-shock system for predefined wave fields. In order to compare these results with those obtained in the scatter-free (i.e., nonwave) case, we restricted particles to a single shock encounter, which is here defined as the period during which the particle remains within a gyrodiameter of the shock. As a particular example, we injected ensembles of ions into a system consisting of a quasi-perpendicular shock moving through the interplanetary spectrum of ambient Alfv¿n waves. As compared with a single encounter in the scatter-free limit, the inclusion of waves (1) increases particle transmission through the shock, (2) produces broader energy distributions for reflected and transmitted particles, with high-energy tails at energies several times the maximum energy obtained in the scatter-free case and (3) reduces anisotropies, particularly of reflected particles, but does not eliminate them. Also, for the range of energies studied, it was found that the approximate invariance of the magnetic moment for particle interactions with quasi-perpendicular shocks is no longer valid when waves are present.