The concept of assemblage has a long history in both the arts and social sciences. Assemblage thinking is particularly useful for critical scholars to engage with complex phenomena, such as drug use and stigma. Analytic methods that support assemblage thinking through the construction, deconstruction, and reconstruction of data-based assemblages are needed. This paper describes a qualitative analytic method, poetic assemblage, that merges the arts and social sciences to support assemblage thinking. I demonstrate its utility by presenting its application to data gathered on the stigma associated with perinatal drug use. Poetic assemblage, a form of poetic inquiry, uses disparate data sources to create temporary constructions that allow the researcher to make and remake connections and relationships across human, nonhuman, and discursive agents. The aim of this paper is to demonstrate how this method can be used to support assemblage thinking and mid-level theorizing around complex and dynamic phenomena. The method involves the evolvement of constructed, deconstructed, and reconstructed research poems. This process creates a liminal space for the researcher to engage with multiple possibilities and allows for a focus on emergent questions rather than on identifying simple answers. Using a series of studies on how healthcare and social services are provided to pregnant and parenting people who use drugs (PPPWUD), I describe my initial use of poetic inquiry in data analysis and my subsequent recognition of its limitations in supporting assemblage thinking. I then demonstrate both the construction and reconstruction of assemblage poems as well as provide examples of analytic insights on structural stigma that were illuminated from the process. While I demonstrate its application to a specific form of stigma, I am proposing the method's utility for imagining new possibilities, identifying emergent questions, and deepening theorizing for any complex social issue.