Perovskites are a class of recently established materials that triggered enormous interest particularly for solar cell applications. Recent studies have pointed out the extraordinary luminescence quantum yield in perovskite materials. The concept of photon recycling investigated in this work promises a route to reharvest the radiatively emitted photons and, thus, lead to an increase in the open-circuit voltage in perovskite solar cells. In this light, this work investigates the role of nanostructured perovskite absorber layers. While the change of the open-circuit voltage due to photon recycling is understood at a conceptional level, the actual impact of a nanostructured interface on the photon recycling has not yet been studied quantitatively. Here, we rely on full-wave optical simulations to quantify the impact of photon recycling on the open-circuit voltage in a nanotextured biperiodic perovskite thin-film layer and additionally with the perovskite layer integrated into a complete solar cell multilayer stack. The validity of the optical simulations is confirmed by far-field measurements of the emission characteristics from fabricated devices. We find that the considered nanostructure provides around 2% increase to a typically achievable open-circuit voltage in perovskite solar cells. We thereby show that, while the main focus for the design of nanostructures is the optimization of light harvesting, photon recycling might be of interest in future designs of solar cell devices.