The rotation rate of a planet is one of its fundamental properties. Saturn's rotation, however, is difficult to determine because there is no solid surface from which to time it, and the alternative 'clock'--the magnetic field--is nearly symmetrically aligned with the rotation axis. Radio emissions, thought to provide a proxy measure of the rotation of the magnetic field, have yielded estimates of the rotation period between 10 h 39 min 22 s and 10 h 45 min 45 s (refs 8-10). Because the period determined from radio measurements exhibits large time variations, even on timescales of months, it has been uncertain whether the radio-emission periodicity coincides with the inner rotation rate of the planet. Here we report magnetic field measurements that revealed a time-stationary magnetic signal with a period of 10 h 47 min 6 s +/- 40 s. The signal appears to be stable in period, amplitude and phase over 14 months of observations, pointing to a close connection with the conductive region inside the planet, although its interpretation as the 'true' inner rotation period is still uncertain.