  The low-luminosity black hole Sgr A* provides a testbed for models of
Radiatively Inefficient Accretion Flows (RIAFs). Recent sub-millimeter linear
polarization measurements of Sgr A* have provided evidence that the electrons
in the accretion flow are relativistic over a large range of radii. Here, we
show that these high temperatures result in elliptical plasma normal modes.
Thus, polarized millimeter and sub-millimeter radiation emitted within RIAFs
will undergo generalized Faraday rotation, a cyclic conversion between linear
and circular polarization. This effect will not depolarize the radiation even
if the rotation measure is extremely high. Rather, the beam will take on the
linear and circular polarization properties of the plasma normal modes. As a
result, polarization measurements of Sgr A* in this frequency regime will
constrain the temperature, density and magnetic profiles of RIAF models.
