We report the presence of a 106-day cycle in the radio variability of Sgr A* based on an analysis of data observed with the Very Large Array (VLA) over the past 20 years. The pulsed signal is most clearly seen at 1.3 cm with a ratio of cycle frequency to frequency width f/ DELTA f= 2.2+/-0.3. The periodic signal is also clearly observed at 2 cm. At 3.6 cm the detection of a periodic signal is marginal. No significant periodicity is detected at both 6 and 20 cm. Since the sampling function is irregular we performed a number of tests to insure that the observed periodicity is not the result of noise. Similar results were found for a maximum entropy method and periodogram with CLEAN method. The probability of false detection for several different noise distributions is less than 5% based on Monte Carlo tests. The radio properties of the pulsed component at 1.3 cm are spectral index alpha 1.0+/- 0.1 (for S\propto nu ^ alpha ), amplitude DELTA S=0.42+/- 0.04 Jy and characteristic time scale DELTA t_FWHM 25+/-5 days. The lack of VLBI detection of a secondary component suggests that the variability occurs within Sgr A* on a scale of 5 AU, suggesting an instability of the accretion disk.