Sgr A* is variable at radio and submillimeter wavelengths on hourly time scales showing time delays between the peaks of flare emission as well as linearly polarized emission at millimeter and sub-mm wavelengths . To determine the polarization characteristics of this variable source at radio frequencies , we present VLA observations of Sgr A* and report the detection of polarized emission at a level of 0.77 \pm 0.01 % and 0.2 \pm 0.01 % at 43 and 22 GHz , respectively . The change in the time averaged polarization angle between 22 and 43 GHz corresponds to a RM of -2.5 \pm 0.6 \times 10 ^ { 3 } rad m ^ { -2 } with no phase wrapping ( or \sim 5 \times 10 ^ { 4 } rad m ^ { 2 } with 2 \pi phase wrap ) . We also note a rise and fall time scale of 1.5 – 2 hours in the total polarized intensity . The light curves of the degree of linearly polarized emission suggests a a correlation with the variability of the total intensity at 43 GHz . The available polarization data at radio and sub-mm wavelengths suggest that the rotation measure decreases with decreasing frequency . This frequency dependence , and observed changes in polarization angle during flare events , may be caused by the reduction in rotation measure associated with the expansion of synchrotron-emitting blobs .