Receptor clustering plays a key role in triggering cellular activation, but the relationship between the spatial configuration of clusters and the elicitation of downstream intracellular signals remains poorly understood. We developed a DNA-origami-based system that is easily adaptable to other cellular systems and enables rich interrogation of responses to a variety of spatially defined inputs. Using a chimeric antigen receptor (CAR) T cell model system with relevance to cancer therapy, we studied signaling dynamics at single-cell resolution. We found that the spatial arrangement of receptors determines the ligand density threshold for triggering and encodes the temporal kinetics of signaling activities. We also showed that signaling sensitivity of a small cluster of high-affinity ligands is enhanced when surrounded by nonstimulating low-affinity ligands. Our results suggest that cells measure spatial arrangements of ligands, translate that information into distinct signaling dynamics, and provide insights into engineering immunotherapies.