Today, an undeniable interest is given to the development of socially intelligent robotic systems and efficient crowd- and socially-aware navigation strategies. In this paper, we introduce a novel crowd-aware navigation algorithm that combines the A* path planner with the Double Deep Q-Network (DDQN) method. The algorithm, named Social A*, aims to allow safe navigation for mobile robots in social dynamics and crowded environments. In order to facilitate future realworld implementation, a new learning environment compatible with the Robot Operating System (ROS) is developed. This allows expert teleoperation to help train the DDQN agent and refine the reward function. We conducted extensive simulations to compare the performance of Social A* with Socially-attentive Reinforcement Learning (SARL*) and Intention Aware Robot Crowd Navigation with Attention-Based Interaction Graph (IARL). The obtained simulation results demonstrate that Social A* not only surpasses SARL* and IARL but also shows enhanced performance in handling static obstacles. These results showcase the excellent crowd-aware navigation performance, the efficiency, and the significant potential of the algorithm.