The recent success of artificial intelligence (AI) systems has been accompanied by a rapid increase in the computational resources needed to successfully train them. This rate of increase threatens the future development of AI systems as they are presently configured. Unsupervised learning, where systems are trained online instead of through offline computation, offers a possible way forward. Here, we present the design of a synaptic circuit made from superconducting electronics capable of spike-timing dependent plasticity (STDP), a form of unsupervised learning. The synapse is constructed from three sub-circuits, each responsible for a part of the synaptic action. We demonstrate the operation of the synapse through numerical simulation and show that it reproduces the hallmark behaviors of STDP. Combined with existing superconducting neuromorphic components like neurons and axons, this synaptic structure could help form a fast, powerful, and energy-efficient Spiking Neural Network.