Measurements by the magnetometer on the Pioneer Venus orbiter have established that during conditions of low solar wind dynamic pressure, large-scale magnetic fields are not present in the ionosphere of Venus but that during conditions of high solar wind dynamic pressure the ionosphere of Venus is magnetized. The source of the magnetic field is thought to be currents induced in the ionosphere by the solar wind. We will show that the ionospheric polarization electric field can act as a source, or ''battery,'' producing a small magnetic field, even without any initial magnetic field. We have calculated this polarization source as a function of altitude and solar zenith angle. The magnetic field was then determined using a two-dimensional kinematic dynamo model of the ionosphere of Venus. The magnetic field attains a maximum strength of about 5 nT at a solar zentih angle of about 120¿. This magnetic field might act as a ''seed'' field for magnetic flux ropes and terminator waves. ¿American Geophysical Union 1992