Rotations of oxygen octahedra are ubiquitous, but they cannot break inversion symmetry in simple perovskites. However, in a layered oxide structure, this is possible, as we demonstrate here in A-site ordered Ruddlesden-Popper NaRTiO4 (R denotes rare-earth metal), previously believed to be centric. By revisiting this series via synchrotron x-ray diffraction, optical second-harmonic generation, piezoresponse force microscopy, and first-principles phonon calculations, we find that the low-temperature phase belongs to the acentric space group P42(1)m, which is piezoelectric and nonpolar. The mechanism underlying this large new family of acentric layered oxides is prevalent, and could lead to many more families of acentric oxides.