The time dependence of the orientation of Earth's inner core relative to the mantle was determined using a recently discovered 10-degree tilt in the axis of symmetry of the inner core's seismic-velocity anisotropy. Two methods of analyzing travel-time variations for rays traversing the inner core, on the basis of 29 years of data from the International Seismological Centre (1964-1992), reveal that the inner core appears to rotate about 3 degrees per year faster than the mantle. An anomalous variation in inner-core orientation from 1969 to 1973 coincides in time with a sudden change ("jerk") in the geomagnetic field.