Self-organized anodization of copper in 0.1 M Na2CO3 electrolyte was studied in order to obtain nanostructured oxide surface on the metal substrate. Linear sweep voltammetry (LSV) revealed that the most suitable voltage range for anodic film formation is from 3 to 31 V. In this range (except between 3 and 7 V), the oxide is formed as nanorods, with the diameter of the anodically grown nanostructures increasing with the applied voltage. The smallest diameter of the nanorods was found to be 28 ± 9 nm (15 V), while the greatest diameter was 109 ± 15 nm (30 V). X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD) and Raman spectroscopy pointed out that the nanorods consist of crystalline CuO (tenorite) and Cu2O (cuprite), and amorphous Cu(OH)2. Moreover, the greater the anodizing voltage, the greater the CuO content versus Cu2O. The formed nanostructured materials may find applications in photocatalysis and catalytic electrochemical reduction of carbon dioxide into light hydrocarbons.