  We obtained rotation measures of 2642 quasars by cross-identification of the
most updated quasar catalog and rotation measure catalog. After discounting the
foreground Galactic Faraday rotation of the Milky Way, we get the residual
rotation measure (RRM) of these quasars. We carefully discarded the effects
from measurement and systematical uncertainties of RRMs as well as large RRMs
from outliers, and get marginal evidence for the redshift evolution of real
dispersion of RRMs which steady increases to 10 rad m$^{-2}$ from $z=0$ to
$z\sim1$ and is saturated around the value at higher redshifts. The ionized
clouds in the form of galaxy, galaxy clusters or cosmological filaments could
produce the observed RRM evolutions with different dispersion width. However
current data sets can not constrain the contributions from galaxy halos and
cosmic webs. Future RM measurements for a large sample of quasars with high
precision are desired to disentangle these different contributions.
