A numerical scheme to perform data assimilation of concentration measurements in Lagrangian models is presented, along with its first implementation called Ocean Plastic Assimilator, which aims to improve predictions of the distributions of plastics over the oceans. This scheme uses an ensemble method over a set of particle dispersion simulations. At each step, concentration observations are assimilated across the ensemble members by switching back and forth between Eulerian and Lagrangian representations. We design two experiments to assess the scheme efficacy and efficiency when assimilating simulated data in a simple double-gyre model. Analysis convergence is observed with higher accuracy when lowering observation variance or using a circulation model closer to the real circulation. Results show that the distribution of the mass of plastics in an area can effectively be improved with this simple assimilation scheme. Direct application to a real ocean dispersion model of the Great Pacific Garbage Patch is presented with simulated observations, which gives similarly encouraging results. Thus, this method is considered a suitable candidate for creating a tool to assimilate plastic concentration observations in real-world applications to estimate and forecast plastic distributions in the oceans. Finally, several improvements that could further enhance the method efficiency are identified.