Cu-doped ZnO thin films with significantly reduced bandgaps were synthesized by incorporation of Cu at room temperature and followed by post-deposition annealing at 500°C in air for 2 hours. All the films were synthesized by RF magnetron sputtering in O2 gas ambient on F-doped tin oxide-coated glass. We found that annealing at 600°C, unlike at 500°C, caused the formation of the CuO phase in the ZnO:Cu films. Optical absorption indicated that some of the Cu in as- grown ZnO:Cu films is metallic. It can be converted into Cu+1 acceptor states by post-deposition annealing at 500°C in air. Mott-Schottky plots, open-circuit response to illumination, and illuminated current-voltage curves along with optical-absorption measurements revealed that ZnO:Cu thin films with p-type conductivity and significantly reduced bandgap were successfully synthesized by Cu incorporation.