  Recent millimeter-VLBI observations of Sagittarius A* (Sgr A*) have, for the
first time, directly probed distances comparable to the horizon scale of a
black hole. This provides unprecedented access to the environment immediately
around the horizon of an accreting black hole. We leverage both existing
spectral and polarization measurements and our present understanding of
accretion theory to produce a suite of generic radiatively inefficient
accretion flow (RIAF) models of Sgr A*, which we then fit to these recent
millimeter-VLBI observations. We find that if the accretion flow onto Sgr A* is
well described by a RIAF model, the orientation and magnitude of the black
hole's spin is constrained to a two-dimensional surface in the spin,
inclination, position angle parameter space. For each of these we find the
likeliest values and their 1-sigma & 2-sigma errors to be a=0(+0.4+0.7),
inclination=50(+10+30)(-10-10) degrees, and position angle=-20(+31+107)(-16-29)
degrees, when the resulting probability distribution is marginalized over the
others. The most probable combination is a=0(+0.2+0.4), inclination=90(-40-50)
degrees and position angle=-14(+7+11)(-7-11) degrees, though the uncertainties
on these are very strongly correlated, and high probability configurations
exist for a variety of inclination angles above 30 degrees and spins below
0.99. Nevertheless, this demonstrates the ability millimeter-VLBI observations,
even with only a few stations, to significantly constrain the properties of Sgr
A*.
