The similarities of quantum turbulence with classical hydrodynamics allow quantum fluids to provide essential models of their classical analog, paving the way for fundamental advances in physics and technology. Recently, experiments on 2D quantum turbulence observed the clustering of same-sign vortices in strong analogy with the inverse energy cascade of classical fluids. However, self-similarity of the turbulent flow, a fundamental concept in the study of classical turbulence, has so far remained largely unexplored in quantum systems. Here, thanks to the unique features of exciton–polaritons, we measure the scale invariance of velocity circulations and show that the cascade process follows the universal scaling of critical phenomena in 2D. We demonstrate this behavior from the statistical analysis of the experimentally measured incompressible velocity field and the microscopic imaging of the quantum fluid. These results can find wide application in both quantum and classical 2D turbulence.