To enhance the detection efficiency of structured vortex beams carrying Orbital Angular Momentum （OAM）, a recognition method combining deep learning with FPGA acceleration is proposed. Random phase screens are generated using the power spectrum inversion method, and five types of atmospheric turbulence conditions are simulated via a spatial light modulator. Vortex beam spot images after passing through the random phase screens are collected to construct a dataset comprising 10,000 samples. A ResNet18 Convolutional Neural Network （CNN） is employed to analyze and compare the impact of different turbulence intensities on OAM mode recognition accuracy. The recognition performance of the model is comprehensively evaluated, and the trained ResNet18 model is subsequently deployed onto a Field-Programmable Gate Array（FPGA） hardware platform for real-time OAM mode recognition. Experimental results demonstrate that under weak and moderate turbulence conditions, the recognition accuracy for three OAM modes reaches 100%, while under strong turbulence, the accuracy for two OAM modes remains as high as 99%, showing a slight decrease compared to the weaker turbulence cases. By deploying the CNN model onto the FPGA platform, the system achieves an energy consumption of 2.844 W, an energy efficiency of 2.19 GOPS/W, and an inference time of 0.58 seconds for OAM mode recognition of vortex beams.