We observe a bistability in an electrically driven polariton condensate, which is manifested by a memory dependent threshold characteristic. In contrast to the polariton bistabilities previously observed in resonantly optically pumped microcavities, our effect occurs under nonresonant electric pumping and is triggered by the current injection scheme. We explain the origin of the bistability by a dependence of the electron-hole tunneling lifetime on the carrier density in the embedded quantum wells. The field screening effect creates a positive feedback loop, which yields the bistable behavior of the condensate. We develop a rate-equation-based model which qualitatively explains the occurrence of the hysteresis under current injection, its reduction with increased magnetic field, and the absence of bistability under optical pumping.