The crystal orientation fabric of glacier ice severely impacts its strength and flow. Crystal fabric is therefore an important consideration when modelling ice flow. Here, we show that shear wave splitting (SWS) of glacial microseismicity can be used to invert for seismic anisotropy and ice fabric at Rutford Ice Stream (RIS). RIS is a fast-flowing Antarctic ice stream, a setting crucial for informing flow models. We present ~2000,000 SWS measurements from glacial microseismicity, registered at a 38-station seismic network located ~40 km upstream the grounding line. A representative subset of this data is inverted for ice fabric. Due to the character of SWS, which accumulates along the ray path, our method works best if additional information on the depth structure of the ice is available, which are radar measurements in our case. We find that the following three-layer model fits the data best: a broad vertical cone near the base of RIS (500 m thick), a thick vertical girdle, orientated perpendicular to flow, in the middle (1200 m thick) and a tilted cone fabric in the uppermost 400 m. Such a fabric causes a depth-dependent strength profile of the ice with the middle layer being ~3.5 times harder to deform along flow than across flow. At the same time, the middle layer is a factor ~16 softer to shear than to compression or extension along flow. If such a configuration is representative for fast-flowing ice streams, it would call for a more complex integration of viscosity in ice sheet models.