Supervised learning, e.g., classification, plays an important role in processing and organizing microblogging data. In microblogging, it is easy to mass vast quantities of unlabeled data, but would be costly to obtain labels, which are essential for supervised learning algorithms. In order to reduce the labeling cost, active learning is an effective way to select representative and informative instances to query for labels for improving the learned model. Different from traditional data in which the instances are assumed to be independent and identically distributed (i.i.d.), instances in microblogging are networked with each other. This presents both opportunities and challenges for applying active learning to microblogging data. Inspired by social correlation theories, we investigate whether social relations can help perform effective active learning on networked data. In this paper, we propose a novel Active learning framework for the classification of Networked Texts in microblogging (ActNeT). In particular, we study how to incorporate network information into text content modeling, and design strategies to select the most representative and informative instances from microblogging for labeling by taking advantage of social network structure. Experimental results on Twitter datasets show the benefit of incorporating network information in active learning and that the proposed framework outperforms existing state-of-the-art methods.