Magneto-ionics is a fast developing research field which opens the perspective of energy efficient magnetic devices, where the magnetization direction is controlled by an electric field which drives the migration of ionic species. In this work, the interfacial perpendicular magnetic anisotropy (PMA) of Pt/Co/oxide stacks covered by ZrO2, acting as a ionic conductor, is tuned by a gate voltage at room temperature. A large variation of the PMA is obtained by modifying the oxidation of the cobalt layer through the migration of oxygen ions: the easy magnetization axis can be switched reversibly from in-plane, with under-oxidized Co, to in-plane, with over-oxidized Co, passing through an out-of-plane magnetization state. The switching time between the different magnetic states is limited by the ion drift velocity. This depends exponentially on the gate voltage, and is varied by over five orders of magnitude, from several minutes to a few ms. The variation of the PMA versus time during the application of the gate voltage can be modeled with a parabolic variation of the PMA and an exponential decrease of the Co oxidation rate. The possibility to explain the observed effect with a simple theoretical model opens the possibility to engineer materials with optimized properties.