Although history may not repeat itself, many human activities are inherently periodic, recurring daily, weekly, monthly, yearly or following some other periods. Such recurring activities may not repeat the same set of keywords, but they do share similar topics. Thus it is interesting to mine topic periodicity from text data instead of just looking at the temporal behavior of a single keyword/phrase. Some previous preliminary studies in this direction prespecify a periodic temporal template for each topic. In this paper, we remove this restriction and propose a simple yet effective framework Torpedo to mine periodic/recurrent patterns from text, such as news articles, search query logs, research papers, and web blogs. We first transform text data into topic-specific time series by a time dependent topic modeling module, where each of the time series characterizes the temporal behavior of a topic. Then we use time series techniques to detect periodicity. Hence we both obtain a clear view of how topics distribute over time and enable the automatic discovery of periods that are inherent in each topic. Theoretical and experimental analyses demonstrate the advantage of Torpedo over existing work.