Artificial intelligence (AI) transforms the ethical and moral subjectivity of teachers, positioning them to navigate the complex convergence of technological advancement, intellectual autonomy, and teacher identity. The purpose of this paper is to offer a conceptual model for how teachers' identities are constituted through AI prompt engineering. Poststructuralist theories are used to examine how the integration of AI in education reshapes the constitution of teachers' identities, drawing from Michel Foucaut's concepts of discourse theory, power/knowledge, governmentality, subjectivities, and technologies of the self. Focusing on three of Foucault's specific technologies of the self--the confessional, the panopticon, and the examination--the paper examines how AI prompt engineering can be considered as a site of governmentality. A conceptual model, "teacher subjectivities constituted through artificial intelligence" (TSCAI), is suggested to illustrate the relationships among the theoretical concepts in a visual format. Reflective questions are posed for teachers to investigate how the model applies to their AI prompt engineering. Implications for practice and research of the TSCAI model are discussed, followed by a recognition of the limitations of the model. The paper concludes with suggestions for using the model in teacher-education contexts and encourages teachers to acknowledge their own identities while working with AI.