Atrial fibrillation (AF) is a prevalent cardiac arrhythmia associated with an elevated risk of severe complications, including stroke and heart failure. Due to its paroxysmal nature and the inherent complexity of electrocardiogram (ECG) signals, developing highly accurate and robust automated detection methods remains a critical challenge. To address the limitations of existing models in simultaneously capturing local morphological anomalies and long-range temporal dependencies, we proposed RT-AFNet, a novel hybrid ResNet-Transformer architecture. Specifically, RT-AFNet integrated the robust local feature extraction capabilities of a Residual Neural Network (ResNet) backbone with the global temporal modeling power of a lightweight self-attention mechanism. Furthermore, a multi-scale feature fusion strategy was introduced to optimize feature representation. The proposed RT-AFNet model was evaluated on three public AF databases: the China Physiological Signal Challenge 2018 (CPSC2018), the PhysioNet/Computing in Cardiology Challenge 2017 (CinC2017), and the MIT-BIH Atrial Fibrillation Database (MIT-BIH AF). The proposed model achieved F1 scores of 99.76%, 97.47%, and 96.20%, along with area under the curve (AUC) values of 99.97%, 98.98%, and 98.28% on the three datasets, respectively. These results demonstrate that the proposed architecture exhibits excellent generalization ability and stability across different databases, providing a robust and reliable deep learning solution for automated AF screening.