Are the Faraday rotating magnetic fields local to intracluster radio galaxies?

We investigate the origin of the high Faraday rotation measures (RMs) found for polarized radio galaxies in clusters. The two most likely origins are magnetic fields local to the source or magnetic fields located in the foreground intracluster medium. The latter is identified as the null hypothesis. Rudnick & Blundell have recently suggested that the presence of magnetic fields local to the source may be revealed in correlations of the position angles (PAs) of the source-intrinsic linear polarization and the RMs. We investigate the claim of Rudnick & Blundell that they have found a relationship between the intrinsic PA(0) of the radio source PKS 1246-410 and its RM by testing the clustering strength of the PA(0)-RM scatter plot. We show that the claimed relationship is an artifact of an improperly performed null experiment. We describe a gradient alignment statistic aimed at finding correlations between PA(0) and RM maps. This statistic does not require any null experiment since it gives a unique (zero) result in the case of uncorrelated maps. We apply it to a number of extended radio sources in galaxy clusters (PKS 1246-410, Cygnus A, Hydra A, and 3C 465). In no case is a significant large-scale alignment of PA(0) and RM maps detected. We find significant small-scale co-alignment in all cases, but we are able to fully identify this with map-making artifacts through a suitable statistical test. We conclude that there is presently no existing evidence for Faraday rotation local to radio lobes. Given the existing independent pieces of evidence, we favor the null hypothesis that the observed Faraday screens are produced by intracluster magnetic fields.