Dynamic soaring is an energy-efficient flight strategy employed by albatrosses to traverse vast oceanic distances by exploiting wind gradients. Inspired by this natural phenomenon, this study proposes a deep reinforcement learning (DRL) framework for real-time trajectory planning of unmanned aerial vehicles (UAVs) performing dynamic soaring. The proposed method enables the UAV to autonomously plan and execute dynamic soaring trajectories, optimizing energy harvesting from the wind while meeting mission-specific requirements. Using the Deep Deterministic Policy Gradient (DDPG) algorithm, the trained agent successfully generates dynamic soaring paths that replicate the Rayleigh loop behavior, effectively harvesting energy while maintaining energy neutrality during flight. The study further identifies an interesting phenomenon where the agent plans windward climb trajectories and successfully harvests energy, which deviates from traditional dynamic soaring models. This discovery highlights the significance of the sideslip angle in energy harvesting, expanding the applicability of conventional dynamic soaring energy mechanisms. The results provide valuable insights into improving UAV dynamic soaring strategies and advancing reinforcement learning applications in energy-efficient autonomous flight.