By simultaneously transducing and amplifying, transistors offer advantages over simpler, electrode-based transducers in electrochemical biosensors. However, transistor-based biosensors typically use static (i.e., DC) operation modes that are poorly suited for sensor architectures relying on the modulation of charge transfer kinetics to signal analyte binding. Thus motivated, here, we translate the AC "pulsed potential" approach typically used with electrochemical aptamer-based (EAB) sensors to an organic electrochemical transistor (OECT). Specifically, by applying a linearly sweeping square-wave potential to an aptamer-functionalized gate electrode, we produce current modulation across the transistor channel two orders of magnitude larger than seen for the equivalent, electrode-based biosensor. Unlike traditional EAB sensors, our aptamer-based OECT (AB-OECT) sensors critically maintain output current even with miniaturization. The pulsed transistor operation demonstrated here could be applied generally to sensors relying on kinetics-based signaling, expanding opportunities for noninvasive and high spatial resolution biosensing.