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With the rapid development of social websites, recent years have witnessed an explosive growth of social images with user-provided tags which continuously arrive in a streaming fashion. Due to the fast query speed and low storage cost, hashing-based methods for image search have attracted increasing attention. However, existing hashing methods for social image retrieval are based on batch mode which violates the nature of social images, i.e., social images are usually generated periodically or collected in a stream fashion. Although there exist many online image hashing methods, they either adopt unsupervised learning which ignore the relevant tags, or are designed in the supervised manner which needs high-quality labels. In this paper, to overcome the above limitations, we propose a new method named Weakly-supervised Online Hashing (WOH). In order to learn high-quality hash codes, WOH exploits the weak supervision by considering the semantics of tags and removing the noise. Besides, We develop a discrete online optimization algorithm for WOH, which is efficient and scalable. Extensive experiments conducted on two real-world datasets demonstrate the superiority of WOH compared with several state-of-the-art hashing baselines.