Conventional full waveform inversion based on the L2 norm is known to suffer from cycle skipping. Numerous techniques have been promoted to face this long term issue, relying on modifications of the function which measures the discrepancy between observed and predicted data. In this study, we propose to measure this discrepancy through the solution of an optimal transport problem. Instead of proceeding to a sample-by-sample comparison of the seismic signal, this offers the possibility to perform a global comparison of the data, taking into account the spatial and time coherency of the predicted and observed shot gathers. The optimal transport problem is reformulated as a non-smooth convex optimization problem, which can be solved efficiently through proximal splitting techniques. As for other modifications of the misfit function, the optimal transport distance is integrated naturally in the FWI workflow through a modification of the adjoint source term. This modified adjoint source is simply the solution of the optimal transport problem. A 2D time-domain acoustic application on the Marmousi 2 model is presented. We show how the sensitivity to the accuracy of the initial model can be reduced using the optimal transport distance.