Differences in the thickness of the high-velocity lid underlying continents as imaged by seismic tomography, have fuelled a long debate on the origin of the 'roots' of continents. Some of these differences may be reconciled by observations of radial anisotropy between 250 and 300 km depth, with horizontally polarized shear waves travelling faster than vertically polarized ones. This azimuthally averaged anisotropy could arise from present-day deformation at the base of the plate, as has been found for shallower depths beneath ocean basins. Such deformation would also produce significant azimuthal variation, owing to the preferred alignment of highly anisotropic minerals. Here we report global observations of surface-wave azimuthal anisotropy, which indicate that only the continental portion of the Australian plate displays significant azimuthal anisotropy and strong correlation with present-day plate motion in the depth range 175-300 km. Beneath other continents, azimuthal anisotropy is only weakly correlated with plate motion and its depth location is similar to that found beneath oceans. We infer that the fast-moving Australian plate contains the only continental region with a sufficiently large deformation at its base to be transformed into azimuthal anisotropy. Simple shear leading to anisotropy with a plunging axis of symmetry may explain the smaller azimuthal anisotropy beneath other continents.