We have measured the dispersion of the gas phase depolarization ratio of Rayleigh scattered light for 12 linear and symmetric top molecules. Combining these data with known refractive index data we obtain the frequency dependence of the polarizability anisotropy. For all molecules studied we find that the polarizability anisotropy increases more rapidly with increasing frequency than the bulk polarizability. We have correlated this behavior with the oscillator strength and direction of the first electronic transition. We have also compared our zero frequency extrapolated anisotropies with the anisotropies determined from static fields with the Kerr effect and the Stark effect in microwave spectroscopy.