  To search for a signature of an intracluster magnetic field, we compare
measurements of Faraday rotation of polarised extragalactic radio sources in
the line of sight of galaxy clusters with those outside. We correlated a
catalogue of 1383 rotation measures (RM) of extragalactic polarised radio
sources with X-ray luminous galaxy clusters from the CLASSIX survey (combining
REFLEX II and NORAS II). We compared the RM in the line of sight of clusters
within their projected radii of r_500 with those outside and found a
significant excess of the dispersion of the RM in the cluster regions. Since
the observed RM is the result of Faraday rotation in several presumably
uncorrelated magnetised cells of the intracluster medium, the observations
correspond to quantities averaged over several magnetic field directions and
strengths. Therefore the interesting quantity is the standard deviation of the
RM for an ensemble of clusters. We found a standard deviation of the RM inside
r_500 of about 120 +- 21 rad m^-2. This compares to about 56 +- 8 rad m^-2
outside. We show that the most X-ray luminous and thus most massive clusters
contribute most to the observed excess RM. Modelling the electron density
distribution in the intracluster medium with a self-similar model, we found
that the dispersion of the RM increases with the column density, and we deduce
a magnetic field value of about 2 - 6 (l/10kpc)^-1/2 microG assuming a constant
magnetic field strength, where l is the size of the coherently magnetised
intracluster medium cells. This magnetic field energy density amounts to a few
percent of the average thermal energy density in clusters. When we assumed the
magnetic energy density to be a constant fraction of the thermal energy
density, we deduced a slightly lower value for this fraction of 3 - 10
(l/10kpc)^-1/2 per mille.
