Polycrystalline Zn1−xCuxO (x = 0.0, 0.02, and 0.05) samples have been prepared using the solid-state reaction procedure. The X-ray diffraction (XRD) patterns of the samples confirm that Cu ions are successfully included in the ZnO hexagonal wurtzite structure. Rietveld analysis of the XRD patterns confirms the phase purity of the synthesized samples and a slight variation in their lattice parameter upon Cu doping. The morphology study by scanning electron microscopy (SEM) depicts transfiguration with Cu doping. The existence of oxygen vacancies (Vo) in the Cu-doped samples is indicated by X-ray photoelectron spectroscopy (XPS). The magnetization measurements reveal the diamagnetic nature of pure ZnO while the Cu-doped samples depict a room-temperature ferromagnetic (RTFM) behavior. The 2% Cu-doped sample shows higher values of both the saturation magnetization and the Vo as compared to the 5% Cu-doped sample. The observed magnetization seems to show a direct relationship with the Vo. The photoluminescence (PL) and ultraviolet (UV) spectroscopic measurements were performed for their optical analysis. The presence of Vo in the Cu-doped samples is revealed by the PL findings also that is in agreement with the XPS results. The UV analysis shows that Cu doping in the ZnO influences the band gap. The observed RTFM induced by Cu doping in ZnO renders it a potential system for spintronic devices useful for energy-efficient data storage devices and energy harvesting eco-friendly applications.