Quadrotor UAVs present considerable challenges for stable flight control due to their nonlinear dynamics and high sensitivity to external disturbances. Traditional PID tuning methods, such as Ziegler-Nichols, often fail to guarantee optimal performance in dynamic and unpredictable environments. This study proposes a Particle Swarm Optimization (PSO) approach for tuning PID controllers in quadrotor UAVs, with a specific focus on hover stabilization. The proposed PSO algorithm optimizes 12 PID parameters (four controllers, each with three gains) and achieves a mean settling time of 0.96 s across five test scenarios, with performance metrics (settling time, overshoot, ITSE, IAE, and RMSE) systematically recorded for each optimization run. Comparative analysis demonstrates that the PSO-tuned controller achieves a 42.3% faster mean settling time (0.96 s vs. 1.66 s) and a 91.2% reduction in overshoot compared to the Ziegler-Nichols method across all test scenarios. This study is based on simulation models and hardware validation remains a key objective for future work.