Sgr A* is a compact radio source at the Galactic Center, thought to be the radiative manifestation of a 2.6* 106 Mo supermassive black hole. At least a portion of its spectrum--notably the mm/sub-mm ``bump''--appears to be produced within the inner portion (r< 10 rS) of a hot, magnetized Keplerian flow, whose characteristics are also consistent with the 10% linear polarization detected from this source at mm wavelengths. (The Schwarzschild radius, rS, for an object of this mass M is 2GM/c2 7.7* 1011 cm, or roughly 1/20 A.U.) The recent detection of a 106-day cycle in Sgr A*'s radio variability adds significant intrigue to this picture, since it may signal a precession of the disk induced by the spin a of the black hole. The dynamical time scale near the marginally stable orbit around an object with this mass is 20 mins. Thus, since the physical conditions associated with the disk around Sgr A* imply rigid-body rotation, a precession period of 106 days may be indicative of a small black hole spin if the circularized flow is confined to a region 30 rS, for which a (M/10) (ro/30 rS)5/2. The precession of a larger structure would require a bigger black hole spin. We note that a small value of a/M (< 0.1) would be favored if the non-thermal ( 1-20 cm) portion of Sgr A*'s spectrum is powered with energy extracted via a Blandford-Znajek type of process, for which the observed luminosity would correspond to an outer disk radius ro 30 rS. Such a small disk size is also suggested by earlier hydrodynamical simulations, and is implied by Sgr A*'s spectral and polarimetric characteristics.