Amyloid formation is now considered a universal and intrinsic property of all proteins, irrespective of their sequences. Therefore, it is interesting to see whether random copolymers of amino acids can also form amyloid aggregates. Here we use a copolymer of 4 amino acids, mimicking the clinically used drug Glatiramer, and demonstrate that it does form amyloid-like fibrils in the aqueous solution despite its random sequence structure. The fibrillar aggregates show an alanine-rich beta-sheet secondary structure, proving the high tolerance of amyloid aggregates to the sequence irregularity in poly(amino acid)s, and suggesting the potential application of random copolymers as amyloid materials.