We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the parameters of the assignment variables in an online setting. The resulting clustering obtained through our probabilistic approach (PRCut) outperforms the Rayleigh quotient relaxation of the combinatorial problem, its online learning extensions, and several widely used methods. We demonstrate that the PRCut clustering has high fidelity to the similarity measure and can perform as well as a supervised classifier when label-based similarities are provided. This novel approach can leverage out-of-the-box self-supervised representations to achieve competitive performance and serve as an evaluation method for the quality of these representations.