  Large-scale coherent magnetic fields in the intergalactic medium are presumed
to play a key role in the formation and evolution of the cosmic web, and in
large scale feedback mechanisms. However, they are theorized to be extremely
weak, in the nano-Gauss regime. To search for a statistical signature of these
weak magnetic fields we perform a cross-correlation between the Faraday
rotation measures of 1742 radio galaxies at $z > 0.5$ and large-scale structure
at $0.1 < z< 0.5$, as traced by 18 million optical and infrared foreground
galaxies. No significant correlation signal was detected within the uncertainty
limits. We are able to determine model-dependent $3 \sigma$ upper limits on the
parallel component of the mean magnetic field strength of filaments in the
intergalactic medium of $\sim 30 \ \mathrm{nG}$ for coherence scales between
$1$ and $2.5 \ \mathrm{Mpc}$, corresponding to a mean upper bound RM
enhancement of $\sim 3.8 \ \mathrm{rad/m^{2}}$ due to filaments along all
probed sight-lines. These upper bounds are consistent with upper bounds found
previously using other techniques. Our method can be used to further constrain
intergalactic magnetic fields with upcoming future radio polarization surveys.
