Seismic instrumentation deployed in boreholes commonly has unknown horizontal orientation. This affects the interpretation of data since the registered amplitude of a seismic wave depends on the orientation of the sensor. I analyzed signals received at borehole seismometers located at Thornton Hospital, La Jolla, CA. Data from the 1999 Hector Mine earthquake are systematically rotated and compared with expected particle motion to determine the absolute orientation of the sensors. Testing of the method using data from surface instruments with known orientation indicates errors on the order of 5%. We then applied the method to data from sensors at depth to determine their orientations.