We investigate the long-term flux density variations of the compact radio source Sgr A∗ at the galactic center by combining recent VLA observations with previous Green Bank interferometer data. We present radio flux density light-curves for Sgr A∗ at 20, 11, 6 and 3.7 cm from 1974 to 1987. Long-term variability with a timescale of at least 5 years is seen at 20 cm and there is evidence for more rapid variations at the shorter wavelengths. The variability timescales at 20, 11 and 6 cm fit the λ2

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... scaling predicted by the theory of refractive scintillation suggesting that the variability could be due to this cause. However, the timescales are relatively short, implying an unusually high velocity in the scattering screen. The modulation index of the variability is large and relatively independent of wavelength.