  We derive the minimal seed magnetic field which unavoidably arises in the
radiation and matter eras, prior to recombination, by the rotational velocity
of ions and electrons, gravitationally induced by the non-linear evolution of
primordial density perturbations. The resulting magnetic field power-spectrum
is fully determined by the amplitude and spectral index of density
perturbations. The rms amplitude of the seed-field at recombination is B ~
10^{-23} (\lambda/Mpc)^{-2} G, on comoving scales larger than about 1 Mpc.
