Deep learning technology has been widely used in synthetic aperture radar automatic target recognition (SAR ATR) tasks due to its good performance and high efficiency. However, the development of semiconductor technology cannot completely satisfy the demand for electronic hardware with high computational capability to conduct deep neural networks. To solve this dilemma, we propose an optronic convolutional neural network (OPCNN) that can perform SAR ATR tasks directly in optical platform. In OPCNN, all computational operations are implemented in optics with high speed and low energy cost. Electronic platforms are used only to control devices and transmit data information without a massive computational burden. As in digital CNNs, the convolutional layer, downsampling layer, nonlinear activation layer, and fully connected layer are all contained in OPCNN. The simulations demonstrate the feasibility of our OPCNN in solving SAR ATR problems. The good performance in experiments, which achieves 87.4% and 93.8% recognition accuracy on original and denoised moving and stationary target acquisition and recognition dataset, validates the application ability of OPCNN in practical scenario. In one-time recognition tasks, the processing time of our OPCNN is only 0.26 s with the speed of light and the power consumption of our prototype is also far less than digital processer, which is 954 W. Through analysis, our OPCNN obtains the higher processing speed and lower energy cost than digital CNNs with the same structure due to the advantages of optical technology. Also, the scalability of optical structure contributes to build more complex networks to solve complicated dataset without the demand of advanced electronic hardware.