  We perform a detailed study of the sensitivity to the anisotropies related to
Dark Matter (DM) annihilation in the Isotropic Gamma-Ray Background (IGRB) as
measured by the Fermi Large Area Telescope (Fermi-LAT). For the first time, we
take into account the effects of the Galactic foregrounds and use a realistic
representation of the Fermi-LAT. We consider DM anisotropies of extra-galactic
origin and of Galactic origin (which can be generated through annihilation in
the Milky Way sub-structures) as opposed to a background of anisotropies
generated by sources of astrophysical origin, blazars for example. We find that
with statistics from 5 years of observation Fermi is sensitive to a DM
contribution at the level of the thermal-relic cross section depending on the
DM mass and annihilation mode. The anisotropy method for DM searches has a
sensitivity comparable to the usual methods based only on the energy spectrum
and thus constitutes an independent and complementary piece of information in
the DM puzzle. (abridged)
