AC optimal power flow (AC OPF) is a challenging task in power system operations due to the nonlinearity and complexity of power systems. In this paper, a new strategy for solving the AC OPF problem is proposed using decomposition and reinforcement learning (RL)-based cutting plane methods. The proposed strategy simplifies the original AC OPF problem by decomposing it into a DC OPF sub-problem and AC power flow (AC PF) calculation sub-problem, while also incorporating linear inequality constraints, or cuts, to limit the feasible region of the DC OPF sub-problem. Subsequently, the power generation profiles obtained from the DC OPF sub-problem are employed for solving AC PF calculation sub-problem. An RL agent is leveraged to estimate the optimal cuts and references for the voltage magnitudes at generator buses. An action selection method is also proposed to reduce the complexity of the agent training and the magnitudes of the variations in the power generations and bus voltages during a time period. Comprehensive case studies are conducted to compare the proposed strategy with the conventional strategies under various test conditions. The results demonstrate that the proposed strategy outperforms the conventional strategies in terms of feasibility and computational efficiency.