Unmanned Aerial Vehicle (UAV)-assisted backscatter communication creates a pivotal architecture for sustainable Internet of Things (IoT) networks. This paper investigates a system where an energy-constrained source harvests energy from a dedicated Radio Frequency (RF) beacon to communicate via a UAV-mounted backscatter relay. We propose a composite channel model that characterizes the dominant Line-of-Sight (LoS) UAV links using Rician fading, while the terrestrial link is modeled under Rayleigh fading. The study’s core contribution is the derivation of exact closed-form expressions for outage probability, enabling precise performance assessment without extensive computational simulations. Validated by Monte Carlo methods, our results highlight that system reliability is critically sensitive to the Rician K-factor. Furthermore, we analyze the time-switching protocol to determine the optimal trade-off between energy harvesting and data transmission durations. These insights provide a theoretical foundation for optimizing practical UAV-backscatter deployments.