Recent seismological studies(1,2) have suggested that the inner core is rotating relative to the bulk of the Earth, a situation which (according to numerical simulations(3)) may be sustained by convective flow in the liquid outer core. On the other hand, large gravitational forces due to the heterogeneous distribution of mass in the Earth’s mantle should be sufficient to keep the inner core aligned with the mantle(4). Here I show that the differential rotation of the inner core can be reconciled with these strong gravitational forces by allowing the shape of the inner core to adjust as it rotates, so permitting an estimate of the effective viscosity of this innermost region of the Earth. The inferred rotation rate constrains the viscosity of the inner core to be less than 10(16) Pa s or greater than 10(20) Pa s, as two different dynamical regimes are possible. The viscosity estimates for these two regimes have very different implications for the origin of seismic anisotropy in the inner core.