Data is central to AI performance, yet its curation remains an invisible and labour-intensive process, often leading to biases and reliability issues. While HCI has explored methods to improve data work, a growing body of research embraces data imperfections in an artistic vein to provoke reflection on human-AI relations. This workshop examines "Data Craft"- practices that creatively manipulate data to challenge conventional AI narratives and lower barriers to public engagement. By framing data craft as a boundary practice, we explore its potential to foster dialogue on AI capabilities, limitations, and societal impact. The workshop will investigate how data craft can be systematically integrated into participatory AI efforts, moving beyond artistic spaces to inform public debate. Through hands-on exploration, we aim to uncover strategies for leveraging data craft to engage diverse communities in shaping AI discourse.