Equilibrium quantum critical points show a universal scaling behavior, captured by the imaginary-time renormalization group (RG) approach. We extend this approach to non-equilibrium systems, by considering steady states of quantum systems coupled to a time-dependent environment. We develop a general real-time RG approach, and identify a novel class of non-equilibrium quantum critical states and phase transitions. As an example, we consider a shunted Josephson junction driven by an external 1/f noise source, and derive its universal scaling of the correlation and response functions.