  We introduce a new mechanism for generating magnetic fields in the
recombination era. This Harrison-like mechanism utilizes vorticity in baryons
that is sourced through the Bose-Einstein condensate of axions via
gravitational interactions. The magnetic fields generated are on the galactic
scales $\sim 10\,{\rm kpc}$ and have a magnitude of the order of
$B\sim10^{-23}\,{\rm G}$ today. The field has a greater magnitude than those
generated from other mechanisms relying on second order perturbation theory,
and is sufficient to provide a seed for battery mechanisms.
