  We study the response of the QCD vacuum to an external magnetic field, in the
presence of strong CP violation. Using chiral perturbation theory and large N_c
expansion, we show that the external field would polarize quantum fluctuations
and induce an electric dipole moment of the vacuum, along the direction of the
magnetic field. We estimate the magnitude of this effect in different physical
scenarios. In particular, we find that the polarization induced by the magnetic
field of a magnetar could accelerate electric charges up to energies of the
order \theta 10^3 TeV. We also suggest a connection with the possible existence
of "hot-spots" on the surface of neutron stars.
