Blind 360°image quality assessment (IQA) aims to predict perceptual quality for panoramic images without a pristine reference. Unlike conventional planar images, 360°content in immersive environments restricts viewers to a limited viewport at any moment, making viewing behaviors critical to quality perception. Although existing scanpath-based approaches have attempted to model viewing behaviors by approximating the human view-then-rate paradigm, they treat scanpath generation and quality assessment as separate steps, preventing end-to-end optimization and task-aligned exploration. To address this limitation, we propose RL-ScanIQA, a reinforcement-learned framework for blind 360°IQA. RL-ScanIQA optimize a PPO-trained scanpath policy and a quality assessor, where the policy receives quality-driven feedback to learn task-relevant viewing strategies. To improve training stability and prevent mode collapse, we design multi-level rewards, including scanpath diversity and equator-biased priors. We further boost cross-dataset robustness using distortion-space augmentation together with rank-consistent losses that preserve intra-image and inter-image quality orderings. Extensive experiments on three benchmarks show that RL-ScanIQA achieves superior in-dataset performance and cross-dataset generalization. Codes are available at https://github.com/wangyuji1/RLScanIQA.git.