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 bbar{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.
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