  This paper examines the detailed sub-milliarcsecond polarization properties
of an individual SiO maser feature displaying a rotation in polarization
electric vector position angle of approximately \pi/2 across the feature. Such
rotations are a characteristic observational signature of circumstellar SiO
masers detected toward a number of late-type, evolved stars. We employ a new
calibration method for accurate circular VLBI polarimetry at millimeter
wavelengths, to present the detailed Stokes {I,Q,U,V} properties for this
feature. We analyze the fractional linear and circular polarization as a
function of projected angular distance across the extent of the feature, and
compare these measurements against several theoretical models proposed for
sharp rotations of electric vector position angle in polarized SiO maser
emission. We find that the rotation is most likely caused by the angle \theta
between the line of sight and a projected magnetic field crossing the critical
Van Vleck angle for maser propagation. The fractional linear polarization
profile m_l(\theta) is well-fit by standard models for polarized maser
transport, but we find less agreement for the fractional circular polarization
profile m_c(\theta).
