A synapse is a junction between two biological neurons, and the strength, or weight of the synapse, determines the communication strength between the neurons. Building a neuromorphic (i.e. neuron isomorphic) computing architecture, inspired by a biological network or brain, requires many engineered synapses. Furthermore, recent investigation in neuromorphic photonics, i.e. neuromorphic architectures on photonics platforms, have garnered much interest to enable high-bandwidth, low-latency, low-energy applications of neural networks in machine learning and neuromorphic computing. We propose a graphene-based synapse model as a core element to enable large-scale photonic neural networks based on on-chip multiwavelength techniques. This device consists of an electro-absorption modulator embedded in a microring resonator. We also introduce an encoding protocol that allows for the representation of synaptic weights on our photonic device with 15.7 bits of resolution using current control hardware. Recent work has suggested that graphene-based modulators could operate in excess of 100 GHz. Combined with our work, such a graphene-based synapse could enable applications for ultrafast and online learning.