  We search for magnetic fields outside galaxies and galaxy clusters by
investigating redshift evolution of Faraday rotation measures (RM) of
extragalactic radio sources. Our analysis reveals a strong evidence for the
redshift dependence of the mean of the absolute value of the RM. The evidence
is further strengthened if the Galactic contribution to the RM is subtracted.
The hypothesis of the absence of the redshift evolution of residual RM is ruled
out at 5 sigma level. The observed redshift dependence of RM is consistent with
the possibility of the presence of nano-Gauss strength magnetic fields with
correlation length shorter than 0.1 Mpc in the weakly overdense elements of the
Large Scale Structure traced by the Ly-alpha clouds.
