Using first-principles calculations, we predict that tunable ferroelectricity can be realized in oxide perovskites with the Grenier structure and ordered oxygen vacancies. Specifically, we show that R_1/3A_2/3FeO_2.67 solids (where R is a rare-earth ion and A an alkaline-earth cation) exhibit polar phases, with a spontaneous polarization tunable by an appropriate choice of R and A. We find that larger cations combined with small R elements lead to a maximum in the polarization and to a minimum in the energy barriers required to switch the sign of the polarization. Ferroelectricity arises from cooperative distortions of octahedral and tetrahedral units, where a combination of rotational and sliding modes controls the emergence of polarization within three-dimensional connected layers. Our results indicate that polar Grenier phases of oxide perovskites are promising materials for microelectronic applications and, in general, for the study of phenomena emerging from breaking inversion symmetry in solids.