  Context. The existence of magnetic fields in the circumgalactic medium (CGM)
is largely unconstrained. Their detection is important as magnetic fields can
have a significant impact on the evolution of the CGM and, in turn, the fields
can serve as tracers for dynamical processes in the CGM. Aims. With Faraday
rotation of polarised background sources, we aim to detect a possible excess of
the rotation measure in the surrounding area of nearby galaxies. Methods. We
use 2,461 residual rotation measures (RRMs) observed with the LOw Frequency
ARray (LOFAR), where the foreground contribution from the Milky Way is
subtracted. The RRMs are then studied around a subset of 183 nearby galaxies
that was selected by apparent $B$-band magnitude. Results. We find that, in
general, the RRMs show no significant excess for small impact parameters (i.e.
the perpendicular distance to the line of sight). However, if we only consider
galaxies at higher inclination angles and sight lines that pass close to the
minor axis of the galaxies, we find significant excess at impact parameters of
less than 100 kpc. The excess in |RRM| is 3.7 $\rm rad\,m^{-2}$ with an
uncertainty between $\pm 0.9~\rm rad\,m^{-2}$ and $\pm 1.3~\rm rad\,m^{-2}$
depending on the statistical properties of the background
(2.8$\sigma$-4.1$\sigma$). With electron densities of ~$10^{-4}~\rm cm^{-3}$
this suggests magnetic field strengths of a few tenths of a micro Gauss.
Conclusions. Our results suggest a slow decrease of the magnetic field strength
with distance from the galactic disc such as expected if the CGM is magnetised
by galactic winds and outflows.
