In this paper we propose a numerical method to approximate the solution of a Backward Stochastic Differential Equations with Jumps (BSDEJ). This method is based on the construction of a discrete BSDEJ driven by a complete system of three orthogonal discrete time-space martingales, the first a random walk converging to a Brownian motion; the second, another random walk, independent of the first one, converging to a Poisson process. The solution of this discrete BSDEJ is shown to weakly converge to the solution of the continuous time BSDEJ. An application to partial integro-differential equations is given.