Gravitational core-mantle coupling may be the cause of the observed variable acceleration of the Earth's rotation on the 1000-year timescale. Density inhomogeneities which randomly come and go in the liquid outer core may gravitationally attract density inhomogeneities in the mantle (and crust), torquing the mantle and changing its rotation state. The corresponding torque by the mantle on the core may also explain the westward drift of the magnetic field of 0.2¿ yr-1. Gravitational core-mantle coupling would stochastically affect the rate of change of the Earth's obliquity by just a few percent. Its contribution to polar wander would only be ~0.5% the presently observed rate.