  The kinetic magnetoelectric effect is an orbital analogue of the Edelstein
effect and offers an additional degree of freedom to control magnetisation via
the charge current. Here we theoretically propose a gigantic kinetic
magnetoelectric effect in topological insulators and interpret the results in
terms of topological surface currents. We construct a theory of the kinetic
magnetoelectric effect for a surface Hamiltonian of a topological insulator,
and show that it well describes the results by direct numerical calculation.
This kinetic magnetoelectric effect depends on the details of the surface,
meaning that it cannot be defined as a bulk quantity. We propose that Chern
insulators and Z_2 topological insulators can be a platform with a large
kinetic magnetoelectric effect, compared to metals by 5 - 8 orders of
magnitude, because the current flows only along the surface. We demonstrate the
presence of said effect in a topological insulator, identifying
Cu$_2$ZnSnSe$_4$ as a potential candidate.
