A recent study of Karato (1999) suggests that deformation induced in the inner core by electromagnetic (Lorentz) forces may account for the development of seismic anisotropy. The viability of this proposal depends on whether Lorentz forces can sustain persistent flow within the inner core. We explore this question by establishing the conditions for static equilibrium when Lorentz forces are present. We find that the requirements for thermodynamic and hydrostatic equilibrium are incompatible at the surface of the inner core. However, the resulting deformation redistributes mass in the interior so as to minimize steady flow. Numerical calculations show that the flow becomes vanishingly weak and is confined to the top of the inner core. Strains in the interior are small and the alignment of crystals is insufficient to explain the anisotropy inferred from seismological observations. ¿ 2000 American Geophysical Union