Most marine plastic pollution originates on land. However, once plastic is at sea, it is difficult to determine its origin. Here we present a Bayesian inference framework to compute the probability that a piece of plastic found at sea came from a particular source. This framework combines information about plastic emitted by rivers with a Lagrangian simulation, and yields maps indicating the probability that a particle sampled somewhere in the ocean originates from a particular source. We applied the framework to the South Atlantic Ocean, focusing on floating river-sourced plastic. We computed the probability as a function of the particle age, at three locations, showing how probabilities vary according to the location and age. We computed the source probability of beached particles, showing that plastic found at a given latitude is most likely to come from the closest source. This framework lays the basis for source attribution of marine plastic.