UAV swarm passive positioning technology only requires the reception of electromagnetic signals to achieve the positioning and tracking of radiation sources. It avoids the active positioning strategy that requires active emission of signals and has the advantages of good concealment, long acting distance, and strong anti-interference ability, which has received more and more attention. In this paper, we propose a new UAV swarm formation flight method based on pure azimuth passive positioning. Specifically, we propose a two-circle positioning model, which describes the positional deviation of the receiving UAV using trigonometric functions relative to the target in polar coordinates. Furthermore, we design a two-step adjustment strategy that enables the receiving UAV to reach the target position efficiently. Based on the above design, we constructed an optimized UAV swarm formation scheme. In experiments with UAV numbers of 8 and 20, compared to the representative comparison strategy, the proposed UAV formation scheme reduces the total length of the UAV formation by 34.76% and 55.34%, respectively. It demonstrates the effectiveness of the proposed method in the application of assigning target positions to UAV swarms.