  We simulate the evolution of the helicity of relic neutrinos as they
propagate to Earth through a realistic model of the Galactic magnetic field,
improving upon the rough estimates in the literature. For magnetic moments
consistent with experimental bounds and several orders of magnitude smaller, we
confirm that the helicity of relic neutrinos and anti-neutrinos rotates so much
that the spin projection changes by $\mathcal{O}$(1). However, as we show, the
total event rate in an inverse tritium beta decay (ITBD) experiment changes by
less than a few percent, unless the lightest neutrino has mass of order 0.001
eV or less. Such a tiny reduction in the absolute rate relative to the standard
model value would be very difficult to establish, even if detecting relic
neutrinos were routine. However as we show, the \emph{directional anisotropy}
of the rate in a \emph{polarized} ITBD detector is $\gtrsim \mathcal{O}$(10\%)
as long as the lightest neutrino mass is $\gtrsim \mathcal{O}$(0.01 eV). Thus
with percent-level error bars on the absolute neutrino flux and its directional
anisotropy, both the mass and magnetic moment of the relic neutrinos can in
principle be probed if they are within a few orders of magnitude of current
bounds.
