Seismic anisotropy provides insight into past episodes of lithospheric deformation and the orientations of strain in the underlying asthenosphere. The Greenland mantle has played host to a rich history of tectonic processes, including multiple orogenies and plume-lithosphere interactions. This study presents new measurements of SKS splitting that reveal strong variations in fast polarization direction with back-azimuth that are consistent across Greenland, including at stations where splitting measurements have not previously been reported. We compared observed fast polarization directions to the predictions of two-layer models with olivine-orthopyroxene anisotropy. The family of models which provides acceptable misfits at 95% confidence indicates an upper layer olivine a-axis azimuth of 226 +/- 2.9{degree sign} and a lower layer olivine a-axis azimuth of 124 +/- 2.7{degree sign} and non-zero axis dips are required. These models are consistent with asthenospheric anisotropy aligned approximately parallel to the direction of plate motion and lithospheric anisotropy due to Proterozoic and Archean orogenic fabrics.