The absolute position of the compact radio source at the dynamical center of the Galaxy, Sgr A^*, was known only to an accuracy of 0.2'' in spite of its accurate location with respect to near-IR stellar sources to within 30 milliarcsecond (mas). To remedy this poor positional accuracy, we have selected 15 high-resolution, high-frequency VLA observations of Sgr A^* carried out in the last 13 years and determined the weighted average position with the average epoch 1992.4 to be at alpha , delta [1950] = 17h 42m 29\dsec3076+/-0.0007, -28^o 59' 18.484+/-0.014'', or alpha , delta [2000] = 17h 45m 40\dsec0383+/-0.0007, -29^o 00' 28.069+/-0.014'' which agrees with earlier published values to within the 0.2'' error bars of the earlier measurements. An accurate absolute position of Sgr A^* can be useful for its identification with sources at other wavelengths, particularly, in soft and hard X-rays with implications for the models of a massive black hole at the Galactic center.