Linear-in-wave-vector K terms of an electron Hamiltonian play an important role in topological insulators and spintronic devices. Here we demonstrate how an external electric field can control the magnitude of a linear-in-K term in the exciton Hamiltonian. The effect of the electric field on interference of exciton polaritons in a high-quality structure with a wide GaAs quantum well was experimentally studied by means of the differential reflection spectroscopy. It is found that the interference pattern is strongly suppressed at certain electric field and then it is reinstalled, but with an inverted phase, at the further increase of the field. This behavior of the pattern is successfully explained by the electric-field-induced linear-in-K terms in the Hamiltonian of the exciton propagating across the quantum well. An excellent agreement between the experimental data and the results of calculations using semiclassical nonlocal dielectric response model confirms the validity of the method and paves the way for the realization of excitonic Datta-Das transistors. In full analogy with the spin-orbit transistor proposed by Datta and Das [Appl. Phys. Lett. 56, 665 (1990)], the switch between positive and negative interference of exciton polaritons propagating forward and backward in a GaAs film is achieved by application of an electric field having a nonzero component in the plane of the quantum well layer.