  The proposition that dark matter halos possess angular momentum, though
widely accepted, is a theoretical prediction which has, till date, not been
observationally verified. The gravi-magnetic field produced by a rotating
gravitating object is possibly the only direct consequence of the angular
momentum of dark matter halos. The gravitational Faraday rotation produced by
the dark matter halo of our galaxy is present in all astronomical observations.
A detection of the imprint of this effect on the all-sky cosmic microwave
background radiation polarisation pattern would directly probe the angular
momentum of the dark matter halo of our Galaxy. We have calculated the expected
gravitational Faraday rotation which turns out to be a $(v_c/c)^3$ effect,
$v_c$ being the rotational speed of our halo. The predicted gravitational
Faraday effect rotation angles are less than $1^{''}$, implying that this
effect, though present, is too small to be detected.
