Deep learning has offered new ideas in SAR ship target recognition. Although many methods improve the recognition performance through the improvement of loss function and migration of deep networks, scattering features as the important intrinsic features of SAR targets, need to be considered in the SAR ship recognition tasks. To introduce the scattering features into the deep network and characterize the features of ship targets more comprehensively, a multi-scale global scattering feature association network (MGSFA-Net) for SAR ship target recognition is proposed in this paper. In the network, the SAR ship target is firstly separated from the background by fine target segmentation. Then, the scattering centers (SCs) of ship targets are extracted and converted to local graph structures based on the k-Nearest Neighbors (KNN) algorithm. The local graph structures are associated by the scattering center feature association (SCFA) module and enhanced by the multi-scale feature enhancement (MSFE) module to produce the multi-scale global scattering features. Moreover, the deep features of the targets are extracted by the multi-kernel deep feature extraction (MKDFE) module to characterize the high-dimensional information. Finally, the scattering features and deep features are fused by weighted integration to enrich the diversity of features. The experimental results on the FUSAR-Ship and OpenSARShip dataset show that, the MGSFA-Net can significantly improve the recognition performance, even on a few-shot condition with the accuracy increasing over 2%-3%. The feature distribution and visualization show the effectiveness of the MGSFA-Net to characterize the multi-scale global scattering association features.