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We present the first measurement of the cross-correlation of weakgravitational lensing and the extragalactic gamma-ray background emission usingdata from the Canada-France-Hawaii Lensing Survey and the Fermi Large AreaTelescope. The cross-correlation is a powerful probe of signatures of darkmatter annihilation, because both cosmic shear and gamma-ray emission originatedirectly from the same DM distribution in the universe, and it can be used toderive constraints on dark matter annihilation cross-section. We show that themeasured lensing-gamma correlation is consistent with a null signal. Comparingthe result to theoretical predictions, we exclude dark matter annihilationcross sections of <sigma v> =10^{-24}-10^{-25} cm^3 s^-1 for a 100 GeV darkmatter. If dark matter halos exist down to the mass scale of 10^-6 M_sun, weare able to place constraints on the thermal cross sections <sigma v> ~ 3 x10^{-26} cm^3 s^-1 for a 10 GeV dark matter annihilation into tau^{+} tau^{-}.Future gravitational lensing surveys will increase sensitivity to probeannihilation cross sections of <sigma v> ~ 5 x 10^{-26} cm^3 s^-1 even for a100 GeV dark matter. Detailed modeling of the contributions from astrophysicalsources to the cross correlation signal could further improve the constraintsby ~ 40-70 %.

Cross-Correlation of Cosmic Shear and Extragalactic Gamma-ray Background: Constraints on the Dark Matter Annihilation Cross-Section