The Askaryan Radio Array (ARA) experiment at the South Pole is designed to detect high-energy neutrinos which, via in-ice interactions, produce coherent radiation at frequencies up to 1000 MHz. In Dec. 2018, a custom high-amplitude radio-frequency transmitter was lowered into the 1700 m SPICE ice core to provide test sources for ARA receiver stations sensitive to vertical and horizontal polarizations. For these tests, signal geometries correspond to obliquely propagating radio waves from below. The ARA collaboration has recently measured the polarization-dependent time delay variation, and report more significant time delays for trajectories perpendicular to ice flow. Here we use fabric data from the SPICE ice core to construct a bounding model for the ice birefringence and the polarization time delays across ARA. The data-model comparison is consistent with the vertical girdle fabric at the South Pole having the prevailing horizontal crystallographic axis oriented near-perpendicular to ice flow. This study presents the possibility that ice birefringence can be used to constrain the range to a neutrino interaction, and hence aid in neutrino energy reconstruction, for in-ice experiments such as ARA.