  Distortions of CMB temperature and polarization anisotropy maps caused by
gravitational lensing, observable with high angular resolution and sensitivity,
can be used to constrain the sterile neutrino mass, offering several advantages
against the analysis based on the combination of CMB, LSS and Ly\alpha forest
power spectra. As the gravitational lensing effect depends on the matter
distribution, no assumption on light-to-mass bias is required. In addition,
unlike the galaxy clustering and Ly\alpha forest power spectra, the projected
gravitational potential power spectrum probes a larger range of angular scales,
the non-linear corrections being required only at very small scales. Taking
into account the changes in the time-temperature relation of the primordial
plasma and the modification of the neutrino thermal potential, we compute the
projected gravitational potential power spectrum and its correlation with the
temperature in the presence of DM sterile neutrino. We show that the
cosmological parameters are generally not biased when DM sterile neutrino is
included. From this analysis we found a lower limit on DM sterile neutrino mass
m_s >2.08 keV at 95% CL, consistent with the lower mass limit obtained from the
combined analysis of CMB, SDSS 3D power spectrum and SDSS Ly\alpha forest power
spectrum ($m_{\nu_s}>1.7$ keV). We conclude that although the information that
can be obtained from lensing extraction is rather limited due to the high level
of the lensing noise of Planck experiment, weak lensing of CMB offers a
valuable alternative to constrain the dark matter sterile neutrino mass.
