Polymer-supported copper catalysts have attained a prominent status and continue to be a focal point of ongoing research and development due to their adaptable properties, which make them invaluable tools for diverse catalytic reactions in aqueous solutions. The objective of this investigation is to develop catalysts supported on a random copolymer that can be assembled in water. A series of random copolymer was prepared through postpolymerization modification of a polymer precursor, poly(pentafluorophenyl acrylate) (PPFPA), employing 1-amino-2-propanol and 1-(3-aminopropyl)imidazole via nucleophilic substitution. Following alkylation and copper insertion, it yielded a polymer-supported copper (Cu) catalyst on poly(N-(2-hydroxypropyl)acrylamide)-ran-poly(N-(3-(1-benzylimidazolium-3-yl)propyl)acrylamide) PHPAM76-ran-PILAM24(Cu(I)), capable of assembling into micellar catalysts in water with a diameter of 175 nm and low polydispersity. These developed self-assembled micelles can serve as nanocatalysts for the copper-catalyzed azide-alkyne cycloaddition (CuAAC) between alkyne and azide derivatives in an aqueous system. Employing PHPAM76-ran-PILAM24(Cu(I)) as the micellar catalyst with a 1 mol % Cu loading significantly enhances reaction yields (95-99%), achieving complete conversion at room temperature within 1-4 h, with minimal copper residue detected in the product (<0.06 ppm) after a straightforward extraction process. This research highlights the versatility of postpolymerization modification of the polymer precursor, PPFPA through nucleophilic substitution as a promising strategy for the development of tailored nanocatalysts for diverse chemical reactions in the future.