We cannot observe the magnetic field inside the earth's core directly, but there is likely to be a large toroidal part of 10--100 Gauss which, together with the dipole component, could produce a magnetic torque on the inner core that tends to rotate it. Estimates based on dynamo calculations give torques of 1019 N m which is large enough to accelerate the inner core to the westward drift velocity of 0.2¿ per year within a few days. Presumably some equilibrium has been reached in which the inner core rotates with constant angular velocity and experiences no net torque. This rotation should have significant consequences for dynamo calculations because it is a very effective method of stretching field lines, and its helps to drive differential rotation in the liquid outer core. The core is modeled by two solid spheres permeated by a uniform field of 5 Gauss representing the dipole. The inner sphere is free to rotate relative to the outer sphere. When a torque of 1019 N m is applied to the inner spere it reaches equilibrium with a steady angular velocity corresponding to a rotation period of 2300 years, which is similar to the westward drift speed, and a toroidal field of about 100 Gauss is induced. The inner sphere can also undergo toroidal oscillations with a period of about 10 years which may be related to the observed secular variation.