Fuhrman cancer grading and tumor-node-metastasis (TNM) cancer staging systems are typically used by clinicians in the treatment planning of renal cell carcinoma (RCC), a common cancer in men and women worldwide. Pathologists typically use percutaneous renal biopsy for RCC grading, while staging is performed by volumetric medical image analysis before renal surgery. Recent studies suggest that clinicians can effectively perform these classification tasks non-invasively by analyzing image texture features of RCC from computed tomography (CT) data. However, image feature identification for RCC grading and staging often relies on laborious manual processes, which is error prone and time-intensive. To address this challenge, this paper proposes a learnable image histogram in the deep neural network framework that can learn task-specific image histograms with variable bin centers and widths. The proposed approach enables learning statistical context features from raw medical data, which cannot be performed by a conventional convolutional neural network (CNN). The linear basis function of our learnable image histogram is piece-wise differentiable, enabling back-propagating errors to update the variable bin centers and widths during training. This novel approach can segregate the CT textures of an RCC in different intensity spectra, which enables efficient Fuhrman low (I/II) and high (III/IV) grading as well as RCC low (I/II) and high (III/IV) staging. The proposed method is validated on a clinical CT dataset of 159 patients from The Cancer Imaging Archive (TCIA) database, and it demonstrates 80% and 83% accuracy in RCC grading and staging, respectively.