A new sustainable heterogeneous catalyst for copper-catalyzed azide-alkyne cycloaddition reaction (CuAAC) was investigated. The preparation of the sustainable catalyst was carried out through the complexation reaction between the polysaccharide cellulose acetate backbone (CA) and copper(II) ions. The resulting complex [Cu(II)-CA] was fully characterized by using different spectroscopic methods such as Fourier-transform infrared spectroscopy (FTIR), Scanning Electron Microscopy (SEM), Energy Dispersive X-ray (EDX), Ultraviolet-visible (UV-vis), and Inductively Coupled Plasma (ICP) analyses. The Cu(II)-CA complex exhibits high activity in the CuAAC reaction for substituted alkynes and organic azides, leading to a selective synthesis of the corresponding 1,4-isomer 1,2,3-triazoles in water as a solvent and working at room temperature. It is worth noting that this catalyst has several advantages from the sustainable chemistry point of view including no use of additives, biopolymer support, reactions carried out in water at room temperature, and easy recovery of the catalyst. These characteristics make it a potential candidate not only for the CuAAC reaction but also for other catalytic organic reactions.