This paper focuses on developing a Deep Reinforcement Learning (DRL)—based agent for real-time trajectory planning and tracking in a simulated parking environment, specifically low-speed maneuvers in a parking area with comb-shaped spaces and a random distribution of non-player vehicles. We rely on CARLA as a virtual driving simulator due to its realistic graphics and physics simulation capabilities, and on the Gymnasium and Stable-Baselines3 toolkits for training the agent. We show that the agent is able to achieve a success rate of 97% in reaching the target parking lot without collisions. However, integrating CARLA with DRL frameworks poses challenges, such as determining suitable environment and neural network update frequencies. Despite these issues, the results demonstrate the potential of DRL agents in developing automated driving functions.