Subretinal injection is a critical procedure for delivering therapeutic agents to treat retinal diseases such as age-related macular degeneration (AMD). However, retinal motion caused by physiological factors such as respiration and heartbeat significantly impacts precise needle positioning, increasing the risk of retinal pigment epithelium (RPE) damage. This paper presents a fully autonomous robotic subretinal injection system that integrates intraoperative optical coherence tomography (iOCT) imaging and deep learning-based motion prediction to synchronize needle motion with retinal displacement. A Long Short-Term Memory (LSTM) neural network is used to predict internal limiting membrane (ILM) motion, outperforming a Fast Fourier Transform (FFT)-based baseline model. Additionally, a real-time registration framework aligns the needle tip position with the robot's coordinate frame. Then, a dynamic proportional speed control strategy ensures smooth and adaptive needle insertion. Experimental validation in both simulation and ex vivo open-sky porcine eyes demonstrates precise motion synchronization and successful subretinal injections. The experiment achieves a mean tracking error below 16.4 μm in pre-insertion phases. These results show the potential of AI-driven robotic assistance to improve the safety and accuracy of retinal microsurgery.