Well-aligned ZnO nanorods were prepared by the vapor phase transport method on Si covered with a ZnO buffer layer. After the nanostructure growth, Cu was doped into the ZnO nanorods by diffusion at three different temperatures and for different times. Undoped and Cu diffusion-doped ZnO samples are highly textured, with the c axis of the wurtzite structure along the growth direction. The incorporation of Cu caused some slight changes in the nanorod alignment, although the wurtzite crystal structure was maintained. X-ray photoelectron spectroscopy measurements revealed that Cu ions were in a divalent state and substituted for the Zn2+ ions of the ZnO matrix. Photoluminescence results at 10 K indicate that the incorporation of copper leads to a relative increase of Cu-related structured green band deep level intensity. Magnetic measurements revealed that both undoped and Cu diffusion-doped ZnO samples exhibited room temperature ferromagnetism. It was also found that bound magnetic polarons play an important role in the appearance of room temperature ferromagnetism in Cu diffusion-doped ZnO nanorods.