  We extend the non-commutative standard model based on the minimal
$SU(3)\times SU(2)\times U(1)$ gauge group to include the interaction of photon
with neutrino. We show that, in the gauge invariant manner, only the right
handed neutrino can directly couple to the photon. Consequently, we obtain the
Feynman rule for the $\gamma\nu\bar\nu$-vertex which does not exist in the
minimal extension of non-commutative standard model (mNCSM). We calculate the
amplitude for $\gamma\nu\to\gamma\nu$ in both the nonminimal non-commutative
standard model (nmNCSM) and the extended version of mNCSM. The obtained cross
section grows in the center of mass frame, respectively, as
$(\theta_{NC})^2{M}_Z^{-4}E^6$ and $(\theta_{NC})^4E^6$ which can exceed the
cross section for $\gamma\nu\to\gamma\gamma\nu$ and $\gamma\nu\to\gamma\nu$ in
the high energy limit in the commutative space.
