In this paper, we demonstrate how studying the rhetorics of ChatGPT prompt writing on social media can promote critical AI literacies. Prompt writing is the process of writing instructions for generative AI tools like ChatGPT to elicit desired outputs and there has been an upsurge of conversations about it on social media. To study this rhetorical activity, we build on four overlapping traditions of digital writing research in computers and composition that inform how we frame literacies, how we study social media rhetorics, how we engage iteratively and reflexively with methodologies and technologies, and how we blend computational methods with qualitative methods. Drawing on these four traditions, our paper shows our iterative research process through which we gathered and analyzed a dataset of 32,000 posts (formerly known as tweets) from X (formerly Twitter) about prompt writing posted between November 2022 to May 2023. We present five themes about these emerging AI literacy practices: (1) areas of communication impacted by prompt writing, (2) micro-literacy resources shared for prompt writing, (3) market rhetoric shaping prompt writing, (4) rhetorical characteristics of prompts, and (5) definitions of prompt writing. In discussing these themes and our methodologies, we highlight takeaways for digital writing teachers and researchers who are teaching and analyzing critical AI literacies.