We present measurements with the VLBA of the variability in the centroid position of \SgrA relative to a background quasar at 7 \mm wavelength. We find an average centroid wander of 71+/- 45 mu as for time scales between 50 and 100 \min and 113+/-50 mu as for timescales between 100 and 200 \min, with no secular trend. These are sufficient to begin constraining the viability of the accretion hot-spot model for the radio variability of \SgrA. It is possible to rule out hot spots with orbital radii above 15 G M_Sgr A*/c2 that contribute more than 30% of the total 7 \mm flux. However, closer or less luminous hot spots remain unconstrained. Since the fractional variability of \SgrA during our observations was 20% on time scales of hours, the hot-spot model for \SgrA's radio variability remains consistent with these limits. Improved monitoring of \SgrA's centroid position has the potential to place significant constraints upon the existence and morphology of inhomogeneities in a supermassive black hole accretion flow.