News tweets that report what is happening have become an important real-time information source. We raise the problem of Semantic Role Labeling (SRL) for news tweets, which is meaningful for fine grained information extraction and retrieval. We present a self-supervised learning approach to train a domain specific SRL system to resolve the problem. A large volume of training data is automatically labeled, by leveraging the existing SRL system on news domain and content similarity between news and news tweets. On a human annotated test set, our system achieves state-of-the-art performance, outperforming the SRL system trained on news.