It is shown that the excitation of charge carriers by ac electric field with zero average driving leads to a direct electric current in quantum well structures. The current emerges for both linear and circular polarization of the ac electric field and depends on the field polarization and frequency. We present a micoscopic model and an analytical theory of such a nonlinear electron transport in quantum wells with structure inversion asymmetry. In such systems, dc current is induced by ac electric field which has both the in-plane and out-of-plane components. The ac field polarized in the interface plane gives rise to a direct current if the quantum well is subjected to an in-plane static magnetic field.