Utilization of Remote Direct Memory Access (RDMA) can offer higher bandwidth, lower latency, and reduced CPU overhead compared to traditional TCP. However, existing feedback-based RDMA congestion control schemes are not effective in addressing the problem of sudden queue accumulation and insufficient bandwidth utilization caused by frequent traffic bursts. In this paper, we propose GTCC, a game theoretic approach for efficient congestion control in RDMA data center networks. This approach enables the transmission rates between distributed senders to approach approximate coordination, thereby reducing the likelihood of network congestion. Firstly, we design a mechanism based on a non-cooperative game model and apply it to data center congestion control. Secondly, considering the limitations of simply introducing a non-cooperative game model, we optimize the game-theoretic approach to better suit data center characteristics. Finally, with the optimized game-theoretic approach, we implement the GTCC congestion control mechanism, improving network metrics in a simple, efficient, and viable manner. We evaluate GTCC using large-scale NS3 simulations. Compared to the standalone deployment of HPCC, GTCC integrated with HPCC shortens Flow Completion Time (FCT) for short flows, with the tail FCT reduced by up to approximately 0.7% to 8.6% in our experiments.