Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks, which are encountered in fundamental areas and real-world practical problems including logistics, social networks, and cryptography. Physical machines have recently been proposed and implemented as an alternative to conventional exact and heuristic solvers for the Ising problem, one such optimization task that requires finding the ground state spin configuration of an arbitrary Ising graph. However, these physical approaches usually suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS) capable of converging to the ground state of various 4-spin graphs with high probability. The INPRIS exploits experimental physical noise as a resource to speed up the ground state search. By injecting additional extrinsic noise during the algorithm iterations, the INPRIS explores larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem, and could thus be implemented with optoelectronic architectures that enable GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), our work paves a way for orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.