Dual-wavelength radio observations during the occultations of Voyagers 1 and 2 provided 3.6-cm and 13-cm data on Saturn's ionospheric irregularies at two locations. Spectra of the weak fluctuations in amplitude and phase can be interpreted using the theory for scattering from a power law spectrum of anisotropic irregularities embedded in a thin screen. Comparisons of measured scintillation spectra with the theory produced least squares solutions for four parameters which characterize the ionospheric irregularities: (1) the axial ratio, (2) the orientation, (3) the power law exponent of the spatial spectrum and (4) the magnitude of the spatial variations in electron density. Scattering was observed from irregularities of approximate size 2--60 km; these lower and upper limits result from noise-limitations and the method of analysis, respectively, and do not represent either an inner or outer scale. Within this range of length scales, the three-dimensional spatial spectrum obeys an inverse power law with exponent near 3.5, and the fractional variations in electron density are about 10--20%. All observaed irregularities appear to be anisotropic with axial ratios greater than 4:1. Magnetic field orientations in Saturn's ionosphere were inferred from the direction of alignment of the anisotropic irregularities. When used as a test of Saturnian magnetic field models, the occultation measurements generally confirm the accuracy of the model predictions but also suggest that a small adjustment of model parameters might improve the field representation.