Salient object detection (SOD) can be applied to consumer electronic area, which can help to identify and locate objects of interest. RGB/RGB-D (depth) salient object detection has achieved great progress in recent years. However, there is a large room for improvement in exploring the complementarity of two-modal information for RGB-T (thermal) SOD. Therefore, this paper proposes a Transformer-based Cross-modal Integration Network (i.e., TCINet) to detect salient objects in RGB-T images, which can properly fuse two-modal features and interactively aggregate two-level features. Our method consists of the siamese Swin Transformer-based encoders, the cross-modal feature fusion (CFF) module, and the interaction-based feature decoding (IFD) block. Here, the CFF module is designed to fuse the complementary information of two-modal features, where the collaborative spatial attention emphasizes salient regions and suppresses background regions of the two-modal features. Furthermore, we deploy the IFD block to aggregate two-level features, including the previous-level fused feature and the current-level encoder feature, where the IFD block bridges the large semantic gap and reduces the noise. Extensive experiments are conducted on three RGB-T datasets, and the experimental results clearly demonstrate the superiority and effectiveness of our method when compared with the cutting-edge saliency methods. The results and code of our method will be available at https://github.com/lvchengtao/TCINet.