Robotic manipulation holds the potential to replace humans in the execution of tedious or dangerous tasks. However, control-based approaches are not suitable due to the difficulty of formally describing open-world manipulation in reality, and the inefficiency of existing learning methods. Thus, applying manipulation in a wide range of scenarios presents significant challenges. In this study, we propose a novel method for skill learning in robotic manipulation called Tactile Active Inference Reinforcement Learning (Tactile-AIRL), aimed at achieving efficient training. To enhance the performance of reinforcement learning (RL), we introduce active inference, which integrates model-based techniques and intrinsic curiosity into the RL process. This integration improves the algorithm's training efficiency and adaptability to sparse rewards. Additionally, we utilize a vision-based tactile sensor to provide detailed perception for manipulation tasks. Finally, we employ a model-based approach to imagine and plan appropriate actions through free energy minimization. Simulation results demonstrate that our method achieves significantly high training efficiency in non-prehensile objects pushing tasks. It enables agents to excel in both dense and sparse reward tasks with just a few interaction episodes, surpassing the SAC baseline. Furthermore, we conduct physical experiments on a gripper screwing task using our method, which showcases the algorithm's rapid learning capability and its potential for practical applications.