The permeability anisotropy that results from a shear displacement $vec{u}$ between the complementary self-affine walls of a rough fracture is investigated. Experiments in which a dyed fluid radially injected into a transparent fracture displaces a transparent one are presented. A clear anisotropy is observed in the presence of shear displacements and allows us to estimate the ratio of the permeabilities for flows parallel and perpendicular to $vec{u}$. A simple model which accounts for the development of channels perpendicular to $vec{u}$ qualitatively explains these results and predicts a permeability decreasing (increasing) linearly with the variance of the aperture field for flow parallel (perpendicular) to the shear displacement. These predictions are then compared to the results of numerical simulations performed using a lattice Boltzmann technique and to the anisotropies measured in displacement experiments.