Oral cancer is known as one of the relatively common malignancy types worldwide. Despite the easy access of the oral cavity to examination, the invasive biopsy is still essential for final diagnosis, which requires laborious operation and complicated trained specialists. With the development of deep learning, the artificial intelligence (AI) technique is applied for oral cancer examinations and alleviates the workload of manual screening on biopsy. However, existing computer-aided oral cancer diagnostic methods focus on oral cavity environment photos and histology images, which require complicated operations for doctors and are invasive and painful for patients. As a noninvasive, real-time imaging technique, optical coherence tomography (OCT) can express sufficient identical information for oral cancer screening, but it has not been effectively explored for automatic oral cancer diagnosis. This paper proposes a novel deep learning method named Local Residual Adaptation Network (LRAN) for noninvasive oral cancer screening on OCT images, collected from 25 patients in Beijing Stomatological Hospital. Our proposed LRAN consists of a Residual Feature Representation (RFR) module and a Local Distribution Adaptation (LDA) module. Specifically, RFR firstly adopts stacked residual blocks as the backbone network to learn feature representations for training data, optimized by the Cross-Entropy loss, and then deploy Euclidean distance to measure the distribution distance between training and testing OCT images. Finally, LRAN achieves distribution-gap bridging by the LDA module, which integrates local maximum mean discrepancy constraint to estimate and minimize the distribution discrepancy between training and testing sets within the same category. We also collected an OCT-based oral cancer image dataset to evaluate the effectiveness of the proposed method, and it achieves an accuracy of 91.62%, a sensitivity of 91.66%, and a specificity of 92.58% on this self-collected dataset. Furthermore, we conduct a quantitative and qualitative analysis, and the results demonstrate LRAN model has excellent capability to solve the noninvasive oral cancer screening task.