We show that the plasma and magnetic fields in the inner region of Saturn's plasma disk rotate in synchronism with the time-variable modulation period of Saturn's kilometric radio emission. This relation suggests that the radio modulation has its origins in the inner region of the plasma disk, most likely from a centrifugally driven convective instability and an associated plasma outflow that slowly slips in phase relative to Saturn's internal rotation. The slippage rate is determined by the electrodynamic coupling of the plasma disk to Saturn and by the drag force exerted by its interaction with the Enceladus neutral gas torus.