  The one-loop helicity amplitudes for the elastic scattering process
$\gamma\nu\to\gamma\nu$ in the Standard Model are computed at high center of
mass energies. A general decomposition of the amplitudes is utilized to
investigate the validity of some of the key features of our results. In the
center of mass, where $\sqrt{s} = 2\omega$, the cross section grows roughly as
$\omega^6$ to near the threshold for $W$-boson production, $\sqrt{s} = m_W$.
Although suppressed at low energies, we find that the elastic cross section
exceeds the cross section for $\gamma\nu\to\gamma\gamma\nu$ when $\sqrt{s}>13 $
GeV. We demonstrate that the scattered photons are circularly polarized and the
net value of the polarization is non-zero. Astrophysical implications of high
energy photon-neutrino scattering are discussed.
