To address the limitations of transmission distance and operational time in ground-based optical fiber and satellite quantum networks, a measurement-device-independent quantum-key-distribution (MDI-QKD) protocol based on photon orbital angular momentum (OAM) encoding with unmanned aerial vehicles (UAVs) as relay platforms is proposed. Leveraging the mobility and controllability of UAVs, a theoretically secure rapid link is established, and the channel robustness is enhanced using photon OAM encoding. By considering factors such as vortex beam expansion and UAV jitter in an analysis, the transmission distance is shown to be affected by state-dependent diffraction (SDD) and pointing errors, thus consequently affecting the key rate. Additionally, the research results indicate that diffraction effects contribute significantly to system performance. Considering both SDD and UAV jitter, the transmission distance can decrease by 58%, which significantly exceeds the effects observed when considering only atmospheric turbulence scattering. This result is used to establish a theoretical model for quantum-key-distribution systems based on UAV relay. This study enhances the comprehensiveness of theoretical analysis and reduces the discrepancy between theoretical analysis and experimental verification, thus providing an important theoretical reference for the development of future UAV-based quantum communication networks.