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 $zsim1$ 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.
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