  We present a correlation between X-ray surface brightness and Faraday
rotation measure in galaxy clusters, both, from radio and X-ray observations as
well as from modeling of the intra-cluster medium. The observed correlation
rules out a magnetic field of constant strength throughout the cluster.
Cosmological, magneto-hydrodynamic simulations of galaxy clusters are used to
show that for a magnetic field of cosmic origin this correlation is expected
and excellently reproduces the observations showing that the RMS scatter of the
Faraday rotation increases linearly with the X-ray surface brightness. From the
correlation between the observable quantities, rotation measure and X-ray
surface brightness, we infer a relation between the physical quantities:
magnetic field and gas density. For the best available observations, those of
A119, we find $B \propto n_e^{0.9}$.
