We have analyzed shear‐wave splitting (SWS) data from local earthquakes in the Permian basin in west Texas to understand crustal stress change and induced seismicity. Two SWS parameters, the fast polarization direction and the delay time, are computed using a semiautomatic algorithm. Most measurements are determined in the Delaware basin and the Snyder area. In both regions, SWS fast directions are mostly consistent with local at stations that are relatively far from the earthquake clusters. Varying fast directions at one station are related to different ray paths and are probably caused by heterogeneity. In the Snyder area, most northeast–southwest fast directions are from the events in the northern part of the cluster, whereas the northwest–southeast fast directions are mostly from the southern part. The northeast–southwest and northwest–southeast fast directions could be attributed to the northeast‐trending normal faults and the northwest‐trending strike‐slip faults, respectively. SWS results in the Delaware basin have two unique features. First, most shallow earthquakes less than 4 km deep produce relatively large delay times. This observation implies that the upper crust of the Delaware basin is highly fractured, as indicated by the increasing number of induced earthquakes. Second, diverse fast directions are observed at the stations in the high‐seismicity region, likely caused by the presence of multiple sets of cracks with different orientations. This situation is possible in the crust with high pore pressure, which is expected in the Delaware basin due to extensive wastewater injection and hydraulic fracturing. We propose that the diversity of SWS fast directions could be a typical phenomenon in regions with a high rate of induced seismicity.