It is an open question how charged particles are injected at quasiperpendicular shocks into a first-order Fermi acceleration mechanism. Cross-field diffusion of solar wind ions is a possible injection process. However, in a system with at least one ignorable spatial dimension, charged particles moving in fluctuating fields are tied to the magnetic field lines. We have therefore determined the cross-field diffusion coefficient of charged particles in self-consistently generated turbulence by three-dimensional hybrid simulations. The initial setup consists of a homogeneous magnetic field with an isotropic core plasma plus a second, nongyrotropic ion distribution. The combined distributions resemble the distribution found immediately downstream of the quasi-perpendicular Earth bow shock: Part of the solar wind is transmitted (core) and part is specularly reflected and subsequently convected downstream (nongyrotropic part). Such a particle distribution excites the Alfv¿n ion cyclotron and mirror mode instability. The turbulence scatters the nongyrotropic ions both parallel and perpendicular to the field. The perpendicular and the parallel diffusion coefficients have been determined for two values of the density of the nongyrotropic distributions, nb. The ratio of the two diffusion coefficients is smaller than the value predicted by hard sphere scattering theory, i.e., parallel scattering is considerably stronger than scattering perpendicular to the field. The power in the magnetic field fluctuations in the high nb case is comparable to the power obtained in a two-dimensional quasi-perpendicular shock simulation immediately behind the shock ramp. On the basis of perpendicular scattering time it is suggested that cross-field diffusion in the turbulent wave field generated by the specularly reflected ions is sufficient to inject and accelerate these ions efficiently at quasi-perpendicular shocks. ¿ 2000 American Geophysical Union