We develop a phase screen model called the Synthetic Aperture Radar (SAR) Scintillation Simulator (SAR-SS) for predicting the impacts of ionospheric scintillation on SAR image formation. SAR-SS consists of a phase screen generator and a propagator. The screen generator creates a 2-D random realization of spatial phase fluctuations resulting from the traversal of small-scale field-aligned irregularities in the ionosphere. It accounts for the motion of the radar platform, the drift of the ionospheric irregularities, and the oblique angle of propagation, all of which determine the scale sizes of the irregularities sampled by the radar beam. The propagator solves the 3-D parabolic wave equation using the split step technique to compute the ionospheric transfer function for two-way propagation. This ionospheric transfer function is used to modulate the SAR signal due to terrestrial features in order to assess the ionospheric impact on SAR image formation in the small target approximation. We compare simulated and observed PALSAR imagery over Brazil during disturbed ionospheric conditions. We demonstrate that SAR-SS can reproduce the field-aligned streaks in PALSAR imagery caused by irregularities in the equatorial ionosphere that have been observed by previous authors. The field-aligned streaks exhibited a dominant wavelength larger than the Fresnel break scale, which suggests that refractive scatter was dominant over diffraction as the physical mechanism responsible for the scintillation of the radar signal in this case. The spectral index of phase fluctuations in the screen was quite large (9.0), suggesting that these irregularities were possibly associated with bottomside sinudoidal irregularities rather than equatorial plasma bubbles.