For controversial topics, collecting argumentation-containing tweets which tend to be more convincing will help researchers analyze public opinions. Meanwhile, claim is the heart of argumentation. Hence, we present the first real-time claim retrieval system CRST that retrieves tweets containing claims for a given topic from Twitter. We propose a claim-oriented ranking module which can be divided into the offline topic-independent learning to rank model and the online topic-dependent lexicon model. Our system outperforms previous claim retrieval system and argument mining system. Moreover, the claim-oriented ranking module can be easily adapted to new topics without any manual process or external information, guaranteeing the practicability of our system.