In this paper we propose a causal modeling approach to intersectional fairness, and a flexible, task-specific method for computing intersectionally fair rankings. Rankings are used in many contexts, ranging from Web search to college admissions, but causal inference for fair rankings has received limited attention. Additionally, the growing literature on causal fairness has directed little attention to intersectionality. By bringing these issues together in a formal causal framework we make the application of intersectionality in algorithmic fairness explicit, connected to important real world effects and domain knowledge, and transparent about technical limitations. We experimentally evaluate our approach on real and synthetic datasets, exploring its behavior under different structural assumptions.