The finding that the Earth's inner core might be rotating faster than the mantle has important implications for our understanding of core processes, including the generation of the Earth's magnetic field. But the reported signal is subtle-a change of about 0.01 s per year in the separation of two seismic waves with differing paths through the core. Subsequent studies of such data have generally supported the conclusion that differential rotation exists, but the difficulty of accurately locating historic earthquakes and possible biases induced by strong lateral variations in structure near the core-mantle boundary have raised doubt regarding the proposed inner-core motion. Also, a study of free oscillations constrained the motion to be relatively small compared to previous estimates and it has been proposed that the interaction of inner-core boundary topography and mantle heterogeneity might lock the inner core to the mantle. The recent detection of seismic waves scattered in the inner core suggests a simple test of inner-core motion. Here we compare scattered waves recorded in Montana, USA, from two closely located nuclear tests at Novaya Zemlya, USSR, in 1971 and 1974. The data show small but coherent changes in scattering which point toward an inner-core differential rotation rate of 0.15 degrees per year-consistent with constraints imposed by the free-oscillation data.