The orientation of ice-crystal grains in glacier ice locally co-evolve with and can enhance the flow of ice. Inferring the grain orientation structure inside glaciers and ice-sheets is therefore essential for improving the accuracy and realism of ice-flow models, with implications for reducing the uncertainty of future sea-level rise projections. In this work, we introduce a new radio-wave model and use it to investigate the extent to which radar surveys over glaciers and ice sheets can reveal the orientation information necessary to improve such ice-flow models. We show that conventional polarimetric radar surveys, where transmitted radio waves are typically incident perpendicular to the surface, might be poorly suited for the task; a configuration that is effectively blind to a specific but important component of the grain orientation structure. We find, however, that radio waves transmitted at an oblique angle to the surface might instead overcome this crucial limitation and allow the sought-after grain orientation information to be inferred.