  We use the TNG50 cosmological magnetohydrodynamical simulation of the
IllustrisTNG project to show that magnetic fields in the circumgalactic medium
(CGM) have significant angular structure. This azimuthal anisotropy at fixed
distance is driven by galactic feedback processes that launch strong outflows
into the halo, preferentially along the minor axes of galaxies. These
feedback-driven outflows entrain strong magnetic fields from the interstellar
medium, dragging fields originally amplified by small-scale dynamos into the
CGM. At the virial radius, $z=0$ galaxies with M$_\star \sim
10^{10}\,\rm{M_\odot}$ show the strongest anisotropy ($\sim 0.35$ dex). This
signal weakens with decreasing impact parameter, and is also present but weaker
for lower mass as well as higher mass galaxies. Creating mock Faraday rotation
measure (RM) sightlines through the simulated volume, we find that the angular
RM trend is qualitatively consistent with recent observational measurements. We
show that rich structure is present in the circumgalactic magnetic fields of
galaxies. However, TNG50 predicts small RM amplitudes in the CGM that make
detection difficult as a result of other contributions along the line of sight.
