Mars has a complex magnetic topology where crustal magnetic fields can interact with the solar wind magnetic field to form magnetic cusps. On the nightside, solar wind electron precipitation can produce enhanced ionization at cusps while closed field regions adjacent to cusps can be devoid of significant ionization. Using an electron transport model, we calculate the spatial structure of the nightside ionosphere of Mars using Mars Global Surveyor electron measurements as input. We find that localized regions of enhanced ionospheric density can occur at magnetic cusps adjacent to low density regions. Under this configuration, thermospheric winds can drive ionospheric electrojets. Collisional ions move in the direction of the neutral winds while magnetized electrons move perpendicular to the wind direction. This difference in motion drives currents and can lead to charge accumulation at the edges of regions of enhanced ionization. Polarization fields drive secondary currents which can reinforce the primary currents leading to electrojet formation. We estimate the magnitude of these electrojets and show that their magnetic perturbations can be detectable from both orbiting spacecraft and the surface. The magnitude of the electrojets can vary on diurnal and annual time scales as the strength and direction of the winds vary. These electrojets may lead to localized Joule heating, and closure of these currents may require field-aligned currents which may play a role in high altitude acceleration processes.