The sweet potato is a plant native to the Americas, and its pre-historic presence in Polynesia is a long-standing anthropological problem. Here we use computer-driven drift simulations to model the trajectories of vessels and seed pods departing from a segment of coast between Mexico and Chile. The experiments demonstrate that accidental drift voyages could have been the mechanism responsible for the pre-historic introduction of the sweet potato from the Americas to Polynesia. While present results do not relate to the feasibility of a transfer by purposeful navigation, they do indicate that this type of voyaging is not required in order to explain the introduction of the crop into Polynesia. The relatively high probability of occurrence and relatively short crossing times of trips from Northern Chile and Peru into the Marquesas, Tuamotu and Society groups are in agreement with the general consensus that this region encompasses the area of original arrival and subsequent dispersal of the sweet potato in Polynesia.