Trust between developers influences the success of open source software (OSS) projects. Although existing research recognizes the importance of trust, there is a lack of an effective and scalable computational method to measure trust in an OSS community. Consequently, OSS project members must rely on subjective inferences based on fragile and incomplete information for trust-related decision making. We propose an automated approach to assist a developer in identifying the trustworthiness of another developer. Our two-fold approach, first, computes direct trust between developer pairs who have interacted previously by analyzing their interactions via natural language processing. Second, we infer indirect trust between developers who have not interacted previously by constructing a community-wide developer network and propagating trust in the network. A large-scale evaluation of our approach on a GitHub dataset consisting of 24,315 developers shows that contributions from trusted developers are more likely to be accepted to a project compared to contributions from developers who are distrusted or lacking trust from project members. Further, we develop a pull request classifier that exploits trust metrics to effectively predict the likelihood of a pull request being accepted to a project, demonstrating the practical utility of our approach.