Synthetic Aperture Radar (SAR) ship target detection has been extensively researched. However, most methods use the same dataset division for both training and validation. In practical applications, it is often necessary to quickly adapt to new loads, new modes, and new data to detect targets effectively. This presents a cross-domain detection problem that requires further study. This paper proposes a method for detecting SAR ships in complex backgrounds using fusion tensor and cross-domain adversarial learning. The method is designed to address the cross-domain detection problem of SAR ships with large differences between the training and test sets. Specifically, it can be used for the cross-domain detection task from the fully polarised medium-resolution ship dataset (source domain) to the high-resolution single-polarised dataset (target domain). This method proposes a channel fusion module (CFM) based on the YOLOV5s model. The CFM utilises the correlation between polarised channel images during training to enrich the feature information of single-polarised images extracted by the model during inference. This article proposes a module called the cross-domain adversarial learning module (CALM) to reduce overfitting and achieve adaptation between domains. Additionally, this paper introduces the anti-interference head (AIH) which decouples the detection head to reduce the conflict of classification and localisation problems. This improves the anti-interference and generalisation ability in complex backgrounds. This paper conducts cross-domain experiments using the constructed medium-resolution SAR full polarisation dataset (SFPD) as the source domain and the high-resolution single-polarised ship detection dataset (HRSID) as the target domain. Compared to the best-performing YOLOV8s model among typical mainstream models, this model improves precision by 4.9%, recall by 3.3%, AP by 2.4%, and F1 by 3.9%. This verifies the effectiveness of the method and provides a useful reference for improving cross-domain learning and model generalisation capability in the field of target detection.