Starting with a randomly distributed sensor array with unknown sensor orientations, array calibration is needed before target localization and tracking can be performed using classical triangulation methods. In this paper, we assume that the sensors are only capable of accurate direction of arrival (DOA) estimation. The calibration problem cannot be completely solved given the DOA estimates alone, since the problem is not only rotationally symmetric but also includes a range ambiguity. Our approach to calibration is based on tracking a single target moving at a constant velocity. In this case, the sensor array can be calibrated from target tracks generated by an extended Kalman filter (EKF) at each sensor. A simple algorithm based on geometrical matching of similar triangles will align the separate tracks and determine the sensor positions and orientations relative to a reference sensor. Computer simulations show that the algorithm performs well even with noisy DOA estimates at the sensors.