Oracle bone inscriptions (OBIs) are a kind of hieroglyph, used about 3,600 years ago for divination and the recording of events. The characters on these OBIs are of great interest because they are precursors to the modern Chinese characters widely used across Asia today. However, as the OBIs were only discovered in 1899, there are currently few documents to describe them. Hence, recognizing and unlocking the meaning of OBIs helps to understand the ancient history of China, the evaluation of Chinese characters, and more. Currently, deep learning has made great progress and brought about a revolution in the research field of recognition, and shows good potential to meet the challenges of OBIs recognition. Due to the scarcity of resources, many OBIs contain only a small number of instances, which causes dataset imbalance and limits the accuracy of recognition. This paper attempts to provide a suite of OBIs recognition methods comprising an original OBIs dataset creation, dynamic dataset augmentation, and a novel deep learning-based recognition method. To this end, we create an original OBIs dataset and propose a modified Generative Adversarial Network for augmenting the original OBIs dataset. The augmented data is then dynamically selected for training the deep learning model considering the data imbalance problem. A novel model called C-A Net is proposed for OBIs recognition. The results of evaluation experiments show that the dynamical dataset augmentation can effectively locate a suitable training dataset for the deep learning model and solve the problem of imbalanced OBIs distribution. In addition, the recognition accuracy of C-A Net is 91.10%, which is higher than that of eight state-of-the-art models, and thus effectively suppresses the occurrence of overfitting. We also present an original OBIs dataset named OBI125, which is currently the only rubbing-type OBIs dataset that is open to the public. The code is available at http://www.ihpc.se.ritsumei.ac.jp/obidataset.html.