Sagittarius A* (Sgr A*) is a strong, compact radio source believed to be powered by a supermassive black hole at the galactic center. Extinction by dust and gas in the galactic plane prevents observing it optically, but its position and proper motion have previously been estimated using radio interferometry. We present new VLBI absolute astrometry measurements of its precise position and proper motion in the frame of the third realization of the International Celestial Reference Frame (ICRF3). The observations used were made at 52 epochs on the VLBA at K band (24 GHz) between 2006 June and 2022 August. We find the proper motion of Sgr A* to be −3.128 ± 0.042 mas yr−1 in R.A. and −5.584 ± 0.075 mas yr−1 in decl., or 6.400 ± 0.073 mas yr−1 at a position angle of 209.°26 ± 0.°51. We also find its J2000 ICRF3 coordinates at the 2015.0 proper motion epoch to be 17h45m40.ˢ034047 ± 0.ˢ000018, −29°00′28.″21601 ± 0.″00044. In galactic coordinates, Sgr A* shows proper motion of −6.396 ± 0.071 mas yr−1 in galactic longitude and −0.239 ± 0.045 mas yr−1 in galactic latitude, indicating solar motion of 248.0 ± 2.8 km s−1 in the galactic plane and 9.3 ± 1.9 km s−1 toward the north galactic pole.