Operation is demonstrated of a field‐effect transistor made of transparant oxidic thin films, showing an intrinsic memory function due to the usage of a ferroelectric insulator. The device consists of a high mobility Sb‐doped n‐type SnO2 semiconductor layer, PbZr0.2Ti0.8O3 as a ferroelectric insulator, and SrRuO3 as a gate electrode, each layer prepared by pulsed laser deposition. The hysteresis behavior of the channel conductance is studied. Using gate voltage pulses of 100 μs duration and a pulse height of ±3 V, a change of a factor of two in the remnant conductance is achieved. The dependence of the conductance on the polarity of the gate pulse proves that the memory effect is driven by the ferroelectric polarization. The influence of charge trapping is also observed and discussed.