Autonomous vision-based perching of quadrotors on moving inclined platforms is critical for air-ground collaboration but remains challenging due to the limited field of view (FOV). In this paper, we propose PerchRL, a reinforcement learning (RL) framework for vision-based agile perching on inclined platforms under rapid and irregular motion. Specifically, we employ a two-stage learning strategy consisting of state-based pre-training followed by vision-based fine-tuning. To improve generalization across diverse platform motions, we employ randomized platform trajectories to prevent overfitting and temporal augmentation methods to capture latent motion patterns from historical observations. During vision-based fine-tuning, a hybrid learning framework consisting of visibility-aware state augmentation and active perception rewards is presented to improve robustness under intermittent visual loss. Extensive simulation and real-world experiments demonstrate the feasibility, stability, and real-time performance of PerchRL, while successful deployment across distinct quadrotor platforms further validates its adaptability. The source code will be released to benefit the community.