It is well known that stacking domains form in moir'e superlattices due to the competition between the interlayer van der Waals forces and intralayer elastic forces, which can be recognized as polar domains due to the local spontaneous polarization in bilayers without centrosymmetry. We propose a theoretical model which captures the effect of an applied electric field on the domain structure. The coupling between the spontaneous polarization and field leads to uneven relaxation of the domains, and a net polarization in the superlattice at nonzero fields, which is sensitive to the moir'e period. We show that the dielectric response to the field reduces the stacking energy and leads to softer domains in all bilayers. We then discuss the recent observations of ferroelectricity in the context of our model.