  Faraday rotation of radio source polarization provides a measure of the
integrated magnetic field along the observational lines of sight. We compare a
new, large sample of Faraday rotation measures (RMs) of polarized extragalactic
sources with galaxy counts in Hercules and Perseus-Pisces, two nearby
superclusters. We find that the average of RMs in these two supercluster areas
are larger than in control areas in the same galactic latitude range. This is
the first RM detection of magnetic fields that pervade a supercluster volume,
in which case the fields are at least partially coherent over several
megaparsecs. Even the most conservative interpretation of our observations,
according to which Milky Way RM variations mimic the background supercluster
galaxy overdensities, puts constraints on the IGM magneto-ionic ``strength'' in
these two superclusters. We obtain an approximate typical upper limit on the
field strength of about 0.3 microGauss l/(500 kpc), when we combine our RM data
with fiducial estimates of electron density from the environments of giant
radio galaxies, and of the warm-hot intergalactic medium (WHIM).
