Cells employ intracellular signaling pathways to sense and respond to changes in their external environment. In recent years, live-cell biosensors have revealed complex pulsatile dynamics in many pathways, but studies of these signaling dynamics are limited by the necessity of live-cell imaging at high spatiotemporal resolution. Here, we describe an approach to infer pulsatile signaling dynamics from a single measurement in fixed cells using a pulse-detecting gene circuit. We computationally screened for circuits with the capability to selectively detect signaling pulses, revealing an incoherent feedforward topology that robustly performs this computation. We implemented the motif experimentally for the Erk signaling pathway using a single engineered transcription factor and fluorescent protein reporter. Our "recorder of Erk activity dynamics" (READer) responds sensitively to spontaneous and stimulus-driven Erk pulses. READer circuits open the door to permanently labeling transient, dynamic cell populations to elucidate the mechanistic underpinnings and biological consequences of signaling dynamics.