The surface charge associated with the spontaneous polarization in ferroelectrics is well known to cause a depolarizing field that can be particularly detrimental in the thin-film geometry desirable for microelectronic devices [1,2]. Incomplete screening of the surface charge, for example by metallic electrodes or surface adsorbates, can lead to the formation of domains [3], suppression or reorientation of the polarization [4], or even stabilization of a higher energy non-polar phase [5]. A huge amount of research and development effort has been invested in understanding the depolarizing behavior and minimizing its unfavorable effects.Here we demonstrate the opposite behavior: A strong polarizing field that drives thin films of materials that are centrosymmetric and paraelectric in their bulk form into a non-centrosymmetric, polar state. We illustrate the behavior using density functional computations for perovskite-structure potassium tantalate, KTaO3, which is of considerable interest for its high dielectric constant, proximity to a quantum critical point and superconductivity. We then provide a simple recipe to identify whether a particular material and film orientation will exhibit the effect, and develop an electrostatic model to estimate the critical thickness of the induced polarization in terms of well-known material parameters. Our results provide practical guidelines for exploiting the electrostatic properties of thin-film ionic insulators to engineer novel functionalities for nanoscale devices.