  Annihilation of dark matter particles in cosmological halos (including a halo
of the Milky Way) contributes to the diffuse gamma-ray background (DGRB). As
this contribution will appear anisotropic in the sky, one can use the angular
power spectrum of anisotropies in DGRB to constrain properties of dark matter
particles. By comparing the updated analytic model of the angular power
spectrum of DGRB from dark matter annihilation with the power spectrum recently
measured from the 22-month data of Fermi Large Area Telescope (LAT), we place
upper limits on the annihilation cross section of dark matter particles as a
function of dark matter masses. We find that the current data exclude <\sigma
v> >~ 10^{-25} cm^3 s^{-1} for annihilation into b\bar{b} at the dark matter
mass of 10 GeV, which is a factor of three times larger than the canonical
cross section. The limits are weaker for larger dark matter masses. The limits
can be improved further with more Fermi-LAT data as well as by using the power
spectrum at lower multipoles (l <~ 150), which are currently not used due to a
potential Galactic foreground contamination.
