  Matter inhomogeneities along the line of sight deflect the cosmic microwave
background (CMB) photons originating at the last scattering surface at redshift
$z \sim 1100$. These distortions modify the pattern of CMB polarization. We
identify specific combinations of Stokes $Q$ and $U$ parameters that correspond
to spin 0,$\pm 2$ variables and can be used to reconstruct the projected matter
density. We compute the expected signal to noise as a function of detector
sensitivity and angular resolution. With Planck satellite the detection would
be at a few $\sigma$ level. Several times better detector sensitivity would be
needed to measure the projected dark matter power spectrum over a wider range
of scales, which could provide an independent confirmation of the projected
matter power spectrum as measured from other methods.
