Space-based synthetic aperture radars (SAR) operating below 1 GHz are subject to forward scattering by ionospheric irregularities. This limits the synthetic aperture and bandwidth over which phase coherence can be maintained. This paper describes the SAR trans-ionospheric radio propagation simulator (SAR-TIRPS), a phase screen model which simulates ionosphere-corrupted SAR images of point targets. The Parabolic Equation propagation method allows both phase and amplitude fluctuations to be modelled. Background Total Electron Content (TEC) is modelled as an additional frequency-dependent phase shift. Examples are presented of L-band and P-band SAR simulations, showing how the target image and derived quantities (sidelobe ratios along- and cross-track) vary with changing ionospheric phase spectrum parameters. SAR-TIRPS proves to be a useful tool in assessing design concepts for low-frequency space radars.