  We report the first detection of magnetic fields associated with the Smith
High Velocity Cloud. We use a catalog of Faraday rotation measures towards
extragalactic radio sources behind the Smith Cloud, new HI observations from
the Green Bank Telescope, and a spectroscopic map of H{\alpha} from the
Wisconsin H-Alpha Mapper Northern Sky Survey. There are enhancements in
rotation measure of approximately 100 rad m^(-2) which are generally well
correlated with decelerated H{\alpha} emission. We estimate a lower limit on
the line-of-sight component of the field of approximately 8 {\mu}G along a
decelerated filament; this is a lower limit due to our assumptions about the
geometry. No RM excess is evident in sightlines dominated by HI or H{\alpha} at
the velocity of the Smith Cloud. The smooth H{\alpha} morphology of the
emission at the Smith Cloud velocity suggests photoionization by the Galactic
ionizing radiation field as the dominant ionization mechanism, while the
filamentary morphology and high (approximately 1 Rayleigh) H{\alpha} intensity
of the lower-velocity magnetized ionized gas suggests an ionization process
associated with shocks due to interaction with the Galactic interstellar
medium. The presence of the magnetic field may contribute to the survival of
high velocity clouds like the Smith Cloud as they move from the Galactic halo
to the disk. We expect these data to provide a test for magnetohydrodynamic
simulations of infalling gas.
