  We report the detection of variable linear polarization from Sgr A* at a
wavelength of 3.5mm, the longest wavelength yet at which a detection has been
made. The mean polarization is 2.1 +/- 0.1% at a position angle of 16 +/- 2 deg
with rms scatters of 0.4% and 9 deg over the five epochs. We also detect
polarization variability on a timescale of days. Combined with previous
detections over the range 150-400GHz (750-2000 microns), the average
polarization position angles are all found to be consistent with a rotation
measure of -4.4 +/- 0.3 x 10^5 rad/m^2. This implies that the Faraday rotation
occurs external to the polarized source at all wavelengths. This implies an
accretion rate ~0.2 - 4 x 10^-8 Msun/yr for the accretion density profiles
expected of ADAF, jet and CDAF models and assuming that the region at which
electrons in the accretion flow become relativistic is within 10 R_S. The
inferred accretion rate is inconsistent with ADAF/Bondi accretion. The
stability of the mean polarization position angle between disparate
polarization observations over the frequency range limits fluctuations in the
accretion rate to less than 5%. The flat frequency dependence of the inter-day
polarization position angle variations also makes them difficult to attribute
to rotation measure fluctuations, and suggests that both the magnitude and
position angle variations are intrinsic to the emission.
