We identify the luminous soft X-ray source AR UMa as a magnetic catacl
ysmic variable containing a white dwarf with the highest field yet det
ected in an accreting binary. IUE and optical spectroscopy, optical ph
otometry, and circular polarimetry and spectropolarimetry define remar
kably distinct accretion states of this binary. Circular polarization
is nearly absent in the high state, but the low state exhibits values
which vary between 2% and 5% on the orbital period of 1.932 hr. The UV
continuum contains a broad absorption feature near 1300 Angstrom, whi
le optical spectropolarimetry during the low state reveals a number of
strongly polarized dips. These are interpreted as Zeeman components o
f hydrogen Ly alpha and another atmospheric species, possibly He I, in
a photospheric magnetic held of similar to 230 MG. The radial velocit
y curve of the low-state optical emission lines shares the period of t
he optical photometry and polarimetry and is phased appropriately for
an origin on the irradiated secondary star. While the high state exhib
its prominent UV line emission typical of the magnetic variables, the
strength of the UV continuum does not vary appreciably with a change i
n accretion state. This, combined with the high soft X-ray luminosity
and lack of circular polarization, indicates that accretion occurs lar
gely in the form of dense filaments which avoid a standoff shock and t
hermalize their kinetic energy below the white dwarf photosphere. We s
uggest that these phenomena may play a role in the apparent lack of hi
gh-field systems with easily detectable circular polarization during h
igh-accretion states.