Accurate estimation and quantification of the corneal nerve fiber tortuosity in corneal confocal microscopy (CCM) is of great importance for disease understanding and clinical decision-making. However, the grading of corneal nerve tortuosity remains a great challenge due to the lack of agreements on the definition and quantification of tortuosity. In this paper, we propose a fully automated deep learning method that performs image-level tortuosity grading of corneal nerves, which is based on CCM images and segmented corneal nerves to further improve the grading accuracy with interpretability principles. The proposed method consists of two stages: 1) A pre-trained feature extraction backbone over ImageNet is fine-tuned with a proposed novel bilinear attention (BA) module for the prediction of the regions of interest (ROIs) and coarse grading of the image. The BA module enhances the ability of the network to model long-range dependencies and global contexts of nerve fibers by capturing second-order statistics of high-level features. 2) An auxiliary tortuosity grading network (AuxNet) is proposed to obtain an auxiliary grading over the identified ROIs, enabling the coarse and additional gradings to be finally fused together for more accurate final results. The experimental results show that our method surpasses existing methods in tortuosity grading, and achieves an overall accuracy of 85.64% in four-level classification. We also validate it over a clinical dataset, and the statistical analysis demonstrates a significant difference of tortuosity levels between healthy control and diabetes group. We have released a dataset with 1500 CCM images and their manual annotations of four tortuosity levels for public access. The code is available at: https://github.com/iMED-Lab/TortuosityGrading.