As the cost and technical difficulty of jamming devices continue to decrease, jamming has become one of the major threats to positioning service. Unfortunately, most conventional technologies are vulnerable to jamming attacks due to their inherent shortcomings like weak signal strength and unfavorable anchor geometry. Thanks to the high operational flexibility, unmanned aerial vehicle (UAV) could fly close to users to enhance signal strength while maintaining a satisfactory geometry, making it a potential solution to the above challenges. In this article, we propose a UAV-assisted anti-jamming positioning system, in which multiple UAVs first utilize time-difference-of-arrival (TDoA) measurements from ground reference stations and double-response two-way ranging (DR-TWR) measurements from UAV-to-UAV links to perform self-localization as well as clock synchronization, and then act as anchor nodes to provide TDoA positioning service for ground users in the presence of jamming. To evaluate the feasibility and performance of the proposed system, we first derive the Cramer-Rao lower bound (CRLB) of UAV self-localization. Then, the impacts of UAV position uncertainty and synchronization errors caused by jamming on positioning service are modeled, and the theoretical root-mean-square error (RMSE) of user position estimate is further derived. Numerical results demonstrate that the proposed system is a promising alternative to existing positioning systems when their services are disrupted by jamming. The most notable advantage of the proposed system is that it is fully compatible with existing user equipment (UE) and positioning methods.