  The extragalactic $\gamma$-ray background and its spatial anisotropy could
potentially contain a signature of dark matter (DM) annihilation or particle
decay. Astrophysical foregrounds, such as blazars and star-forming galaxies
(SFGs), however, dominate the $\gamma$-ray background, precluding an easy
detection of the signal associated with the DM annihilation or decay in the
background intensity spectrum. The DM imprint on the $\gamma$-ray background is
expected to be correlated with large-scale structure tracers. In some cases,
such a cross-correlation is even expected to have a higher signal-to-noise
ratio than the auto-correlation. One reliable tracer of the DM distribution in
the large-scale structure is lensing of the cosmic microwave background (CMB),
and the cosmic infrared background (CIB) is a reliable tracer of SFGs. We
analyze Fermi-LAT data taken over 92 months and study the cross-correlation
with Planck CMB lensing, Planck CIB, and Fermi-$\gamma$ maps. We put upper
limits on the DM annihilation cross-section from the cross-power spectra with
the $\gamma$-ray background anisotropies. The unbiased power spectrum
estimation is validated with simulations that include cross-correlated signals.
We also provide a set of systematic tests and show that no significant
contaminations are found for the measurements presented here. Using
$\gamma$-ray background map from data gathered over 92 months, we find the best
constraint on the DM annihilation with a $1\sigma$ confidence level upper limit
of $10^{-25}$-$10^{-24}$ cm$^{3}$ s$^{-1}$, when the mass of DM particles is
between 20 and 100 GeV.
