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In airborne radargrams, undulating periodic patterns in amplitude that overprint traditional radiostratigraphic layering are occasionally observed, however, they have yet to be analyzed from a geophysical or glaciological perspective. We present evidence supported by theory that these depth‐periodic patterns are consistent with a modulation of the received radar power due to the birefringence of polar ice, and therefore indicate the presence of bulk fabric anisotropy. Here, we investigate the periodic component of birefringence‐induced radar power recorded in airborne radar data at the eastern shear margin of Thwaites Glacier and quantify the lateral variation in azimuthal fabric strength across this margin. We find the depth variability of birefringence periodicity crossing the shear margin to be a visual expression of its shear state and its development, which appears consistent with present‐day ice deformation. The morphology of the birefringent patterns is centered at the location of maximum shear and observed in all cross‐margin profiles, consistent with predictions of ice fabric when subjected to simple shear. The englacial fabric appears stronger inside the ice stream than outward of the shear margin. The detection of birefringent periodicity from non‐polarimetric radargrams presents a novel use of subsurface radar to constrain lateral variations in fabric strength, locate present and past shear margins, and characterize the deformation history of polar ice sheets.