Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks such as the Ising problem, which requires finding the ground state spin configuration of an arbitrary Ising graph. Physical Ising machines have recently been developed as an alternative to conventional exact and heuristic solvers; however, these machines typically 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), using the silicon-on-insulator process, that is capable of converging to the ground state of various 4-spin graphs with high probability. The INPRIS exploits noise as a resource to speed up the ground state search and to explore 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, therefore, compatible with optoelectronic architectures that support GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), this work paves a way for orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.