Cooperative multi-agent reinforcement learning (MARL) demands principled mechanisms to align heterogeneous policies while preserving the capacity for specialized behavior. We introduce a novel consensus framework that defines the team strategy as the entropic-regularized p-Wasserstein barycenter of agents' joint state--action visitation measures. By augmenting each agent's policy objective with a soft penalty proportional to its Sinkhorn divergence from this barycenter, the proposed approach encourages coherent group behavior without enforcing rigid parameter sharing. We derive an algorithm that alternates between Sinkhorn-barycenter computation and policy-gradient updates, and we prove that, under standard Lipschitz and compactness assumptions, the maximal pairwise policy discrepancy contracts at a geometric rate. Empirical evaluation on a cooperative navigation case study demonstrates that our OT-barycenter consensus outperforms an independent learners baseline in convergence speed and final coordination success.