An algorithm is presented which estimates the rotation speed of an orbiting point in spotlight-mode synthetic aperture radar (SAR) systems. Current reconstruction algorithms for spotlight-mode SAR assume that the relative motion between radar and the object is known at all time instants. Although this is true, for example, for airborne terrain mapping radar, the assumption may not apply to all cases. For ground-based radar which is imaging an unidentified space object such as a satellite, the rotation speed of the object is usually unknown. Furthermore, for computer vision applications it is also very important to estimate the rotation speed for the purpose of motion estimation. The new algorithm can accurately estimate the rotation speed in most cases. Simulation results show that the average estimation error is less then 0.78%. For 99.33% of the cases, the estimation error is less than 3%. In the worst case, the error is still less than 6.68%.