Millimeter polarimetry of Sgr A* probes the linearly polarized emission region on a scale of $sim 10$ Schwarzschild radii ($R_S$) as well as the dense, magnetized accretion flow on scales out to the Bondi radius ($sim 10^5 R_S$) through Faraday rotation. We present here multi-epoch ALMA Band 6 (230 GHz) polarimetry of Sgr A*. The results confirm a mean rotation measure, ${rm RM} approx -5 times 10^5 {rm rad m^{-2}}$, consistent with measurements over the past 20 years and support an interpretation of the RM as originating from a radiatively inefficient accretion flow (RIAF) with $dot{M} approx 10^{-8} { rm M_{odot} y^{-1} }$. Variability is observed for the first time in the RM on time scales that range from hours to months. The long-term variations may be the result of changes in the line of sight properties in a turbulent accretion flow. Short-term variations in the apparent RM are not necessarily the result of Faraday rotation and may be the result of complex emission and propagatation effects close to the black hole, some of which have been predicted in numerical modeling. We also confirm the detection of circular polarization at a mean value of $-1.1 pm 0.2 %$. It is variable in amplitude on time scales from hours to months but the handedness remains unchanged from that observed in past centimeter- and millimeter-wavelength detections. These results provide critical constraints for the analysis and interpretation of Event Horizon Telescope data of Sgr A*, M87, and similar sources.
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