  We show that axion domain wall is ferromagnetic in the universe with
nonvanishing baryon number or lepton number. It is caused by protons and
electrons bounded to the domain wall with their spins aligned. These bound
states arise due to attractive potentials generated through pseudo-vector
couplings between the fermions and the axion. Using a model of hadronic axions
we predict existence of a primordial magnetic field with strength $10^{-13}$
Gauss at recombination.
