Insights gained from quantum physics can inspire novel classical technologies. These quantum-inspired technologies are protocols that aim at mimicking particular features of quantum algorithms. They are generally easier to implement and make use of intense beams. Here we demonstrate in a proof-of-concept experiment a quantum-inspired protocol based on the idea of quantum fingerprinting (Phys. Rev. Lett. 87, 167902, 2001).The carriers of information are optical beams with orbital angular momentum (OAM). These beams allow the implementation of a Fredkin gate or polarization-controlled SWAP operation that exchanges data encoded on beams with different OAM. We measure the degree of similarity between waveforms and strings of bits without unveiling the information content of the data.