Cellular-connected unmanned aerial vehicles (UAVs) have gained increasing attention due to their potential to enhance conventional UAV capabilities by leveraging existing cellular infrastructure for reliable communications between UAVs and base stations. They have been used for various applications, including weather forecasting and search and rescue operations. However, under extreme weather conditions such as rainfall, it is challenging for the trajectory design of cellular UAVs, due to weak coverage regions in the sky, limitations of UAV flying time, and signal attenuation caused by raindrops. To this end, this paper proposes a physics-based trajectory design approach for cellular-connected UAVs in rainy environments. A physics-based electromagnetic simulator is utilized to take into account detailed environment information and the impact of rain on radio wave propagation. The trajectory optimization problem is formulated to jointly consider UAV flying time and signal-to-interference ratio, and is solved through a Markov decision process using deep reinforcement learning algorithms based on multi-step learning and double Q-learning. Optimal UAV trajectories are compared in examples with homogeneous atmosphere medium and rain medium. Additionally, a thorough study of varying weather conditions on trajectory design is provided, and the impact of weight coefficients in the problem formulation is discussed. The proposed approach has demonstrated great potential for UAV trajectory design under rainy weather conditions.