Recently, hashing video contents for fast retrieval has received increasing attention due to the enormous growth of online videos. As the extension of image hashing techniques, traditional video hashing methods mainly focus on seeking the appropriate video features but pay little attention to how the video-specific features can be leveraged to achieve optimal binarization. In this paper, an end-to-end hashing framework, namely Unsupervised Deep Video Hashing (UDVH), is proposed, where feature extraction, balanced code learning and hash function learning are integrated and optimized in a self-taught manner. Particularly, distinguished from previous work, our framework enjoys two novelties: 1) an unsupervised hashing method that integrates the feature clustering and feature binarization, enabling the neighborhood structure to be preserved in the binary space; 2) a smart rotation applied to the video-specific features that are widely spread in the low-dimensional space such that the variance of dimensions can be balanced, thus generating more effective hash codes. Extensive experiments have been performed on two real-world datasets and the results demonstrate its superiority, compared to the state-of-the-art video hashing methods. To bootstrap further developments, the source code will be made publically available.