Protein phosphorylation signaling networks have a central role in how cells sense and respond to their environment. We engineered artificial phosphorylation networks in which reversible enzymatic phosphorylation cycles were assembled from modular protein domain parts and wired together to create synthetic phosphorylation circuits in human cells. Our design scheme enabled model-guided tuning of circuit function and the ability to make diverse network connections; synthetic phosphorylation circuits can be coupled to upstream cell surface receptors to enable fast-timescale sensing of extracellular ligands, and downstream connections can regulate gene expression. We engineered cell-based cytokine controllers that dynamically sense and suppress activated T cells. Our work introduces a generalizable approach that allows the design of signaling circuits that enable user-defined sense-and-respond function for diverse biosensing and therapeutic applications.