A mechanism is considered for oxide growth on an electrically isolated metal sample in the presence of an rf-excited oxygen plasma. The assumption is made that the rate of rf oxidation is limited by transport of ionic species through the already-formed oxide layer. Thermally activated hopping of ionic defects in the presence of electric fields due to the surface potential established by the rf discharge and modified by the space charge of the mobile ionic defects is hypothesized. The origin of the voltage across the oxide is discussed in terms of a balance between the transport of negatively charged O ions and transport of electron holes created by ion neutralization of positive ions from the plasma. This model is developed analytically and evaluated numerically by employing the continuum limit of hopping transport equations valid for the very-high-field limit. A three parameter fit gives excellent agreement of the theory with the published data of Greiner for the rf oxidation of lead. The fitting parameters are the voltage across the oxide film, the ionic diffusivity, and the rate at which the oxide is removed by sputtering. The resulting parameter values are shown to be in reasonable accord with available experimental data. Parametric curves are presented to illustrate the dependence of the kinetics on the various microscopic parameters. The dependence of the limiting thickness on the primary parameters is likewise presented. It is shown that the growth rate may be significantly retarded by high levels of space charge in the oxide.