Teleseismic SKS data collected by a temporary broadband array across western Tibet are analysed to constrain shear-wave splitting parameters. Small delay anisotropy is detected, with a rotation of the fast axis azimuth from 40 degrees E in the Tarim basin west of Yecheng to more easterly values between Hotien and Shiquanhe. A large contribution of crustal anisotropy would be required to link fast axis directions orthogonal to the Kunlun and Karakorum ranges with crustal shear due to underthrusting. The fast axes north of Yecheng may instead reflect frozen Proterozoic strain in the Tarim lithosphere. The E-W direction south of Hotien may be related to sinistral shear along the Altyn Tagh fault. It is possible that fast axes directions south of this fault reflect northeastwards motion of Tibet relative to Asia.