  Neutrino capture on tritium has emerged as a promising method for detecting
the cosmic neutrino background (CvB). We show that relic neutrinos are captured
most readily when their spin vectors are anti-aligned with the polarization
axis of the tritium nuclei and when they approach along the direction of
polarization. As a result, CvB observatories may measure anisotropies in the
cosmic neutrino velocity and spin distributions by polarizing the tritium
targets. A small dipole anisotropy in the CvB is expected due to the peculiar
velocity of the lab frame with respect to the cosmic frame and due to late-time
gravitational effects. The PTOLEMY experiment, a tritium observatory currently
under construction, should observe a nearly isotropic background. This would
serve as a strong test of the cosmological origin of a potential signal. The
polarized-target measurements may also constrain non-standard neutrino
interactions that would induce larger anisotropies and help discriminate
between Majorana versus Dirac neutrinos.
