This dissertation examines an emerging "engaged rhetoric of science, technology, and medicine" (ERSTM)---an effort to ensure rhetoric's "broader impacts" by more directly engaging the practices of science and sociotechnical policymaking. Through careful analysis of engaged rhetorical practice, I identify divergent conceptualizations of both rhetoric and engagement and subsequently draw on new materialist rhetorical theory and empirical research on science communication and public engagement to advance "problem-oriented rhetorical catalysis" (PRC) as a mode of engagement capable of advancing rhetoric's institutional value and ethical commitments without abandoning its core disciplinary expertise and areas of inquiry. I further suggest the PRC is uniquely suited to address "wicked problems" and as such represents a productive alternative to deficit- and transmission-model engagement.