  We derive the cross section of neutrino-nucleon scatterings in supernova
magnetic fields, including weak-magnetism and recoil corrections. Since the
weak interaction violates the parity, the scattering cross section
asymmetrically depends on the directions of the neutrino momenta to the
magnetic field; the origin of pulsar kicks may be explained by the mechanism.
An asymmetric neutrino emission (a drift flux) due to neutrino-nucleon
scatterings is absent at the leading level of $\mathcal O(\mu_BB/T)$, where
$\mu_B$ is the nucleon magneton, $B$ is the magnetic field strength, and $T$ is
the matter temperature at a neutrinosphere. This is because at this level the
drift flux of the neutrinos are exactly canceled by that of the antineutrinos.
Hence, the relevant asymmetry in the neutrino emission is suppressed by much
smaller coefficient of $\mathcal O(\mu_BB/m)$, where $m$ is the nucleon mass;
detailed form of the relevant drift flux is also derived from the scattering
cross section, using a simple diffusion approximation. It appears that the
asymmetric neutrino emission is too small to induce the observed pulsar kicks.
However, we note the fact that the drift flux is proportional to the deviation
of the neutrino distribution function from the value of thermal equilibrium at
neutrinosphere. Since the deviation can be large for non-electron neutrinos, it
is expected that there occurs cancellation between the deviation and the small
suppression factor of $\mathcal O(\mu_BB/m)$. Using a simple parameterization,
we show that the drift flux due to neutrino-nucleon scatterings may be
comparable to the leading term due to beta processes with nucleons, which has
been estimated to give a relevant kick velocity when the magnetic field is
sufficiently strong as $10^{15}$--$10^{16}$ G.
