We studied several thousand electron density profiles from the Mars Global Surveyor Radio Science experiment. Electron densities in some of these profiles change significantly over vertical distances as short as 1--2 km, often causing localized bite-outs. These anomalous profiles are preferentially located above crustal magnetic anomalies. Anomalous features and their association with strong magnetic fields are also seen in profiles from Mariner 9. The probability of a profile being anomalous depends on the orientation of the magnetic field, suggesting localized electrodynamic effects upon otherwise global photochemical ionospheric processes. On Mars, unlike most other planets, the magnetic field has a short characteristic lengthscale, so its effects on the ionosphere will vary over short horizontal distances. We discuss possible ionospheric dynamo processes and encourage additional ionospheric observations over regions of strong crustal magnetic field.