  We calculate the cross section of the inverse beta decay process, $\nu_e+n\to
p+e$, in a background magnetic field which is much smaller than $m_p^2/e$.
Using exact solutions of the Dirac equation in a constant magnetic field, we
find the cross section for arbitrary polarization of the initial neutrons. The
cross section depends on the direction of the incident neutrino even when the
initial neutron is assumed to be at rest and has no net polarization. Possible
implications of the result are discussed.
