Ice cores in Antarctica and Greenland reveal ice-crystal fabrics that can be softer under simple shear compared with isotropic ice. Due to the sparseness of ice cores in regions away from the ice divide, we currently lack information about the spatial distribution of ice fabrics and its association with ice flow. Radio-wave reflections are influenced by ice-crystal alignments, allowing them to be tracked provided reflections are recorded simultaneously in orthogonal orientations (polarimetric measurements). Here, we image spatial variations in the thickness and extent of ice fabric across Dome A in East Antarctica, by interpreting polarimetric radar data. We identify four prominent fabric units, each several hundred meters thick, extending over hundreds of square km. By tracing internal ice-sheet layering to the Vostok ice core, we are able to determine the approximate depth-age profile at Dome A. The fabric units correlate with glacial-interglacial cycles, most noticeably revealing crystal alignment contrasts between the Eemian and the glacial episodes before and after. The anisotropy within these fabric layers has a spatial pattern determined by ice flow over subglacial topography.