Dual frequency radio occultation experiments carried out with Voyagers 1 and 2 provided data on the spatial irregularities in Jupiter's ionosphere at four different locations. Sample spectra of weak fluctuations in amplitude and phase of the 3.6-cm and 13-cm wavelength radio signals can be interpreted by using the theory for scattering from an anisotropic power law phase screen. Least squares solutions for ionospheric parameters derived from the observed fluctuation spectra yielded estimates of (1) the axial ratio, (2) angular orientation of the anisotropic irregularities, (3) the power law exponent of the spatial spectrum of irregularities, and (4) the magnitude of the spatial variations in electron density. Equipment limitations and the method of analysis constrain the observations to irregularities of approximate size 1--200 km. No evidence of the inner or outer scale of the irregularities was found. For length scales in the range given, the three-dimensional spatial spectrum obeys a power law with exponent varying from -3.0 to -3.7, and the root mean square fractional variations in electron density are 1--15%. All observed irregularities appear to be anisotropic with axial ratios between 2:1 and 10:1. Ionospheric parameters vary with altitude and latitude. We conclude that the measured angular orientation of the anisotropic irregularities indicates magnetic field direction and may provide a basis for refining Jovian magnetic field models.