Critical safety requirements necessitate ultra-high precision quality control during the assembly of large aerospace components to reduce the mismatch between parts to be joined. Traditional methods use heuristic shape adjustment or surrogate model-based control. These methods are limited by reliance on accurate model learning and inadequate robustness to varying initial assembly conditions. To address these limitations, this paper proposes a model-free reinforcement learning approach for adaptive fuselage shape control during aircraft assembly. The trained reinforcement learning agent directly adjusts the aircraft components in response to their part variations and enables an autonomous system (like AlphaGo) to learn the optimal shape control policy. Specifically, the reinforcement learning environment is built on the finite element simulator. A reward function is developed to capture the optimization objective and introduces a scheme to enforce the original constraints. The proximal policy optimization algorithm is modified to speed up the learning progress and achieve better final performance. In the case study, the root-mean-square gap between components is reduced by 98.4% on average compared with their initial shape mismatch. Our proposed method outperforms the benchmark methods with smaller final shape errors, smaller maximum forces, and lower variations across different test samples.