The curing of thermoset resins is a critical step in the manufacturing of thermoset polymer matrix composites, determining the ultimate mechanical properties of the material, and accounting for a significant fraction of the cost of manufacturing. The use of in-situ cure monitors will permit adaptive control of the cure process, thereby lowering energy costs, reducing scrap rate, and optimizing mechanical properties. We describe here the design and demonstration of an embeddable fiber optic sensor to measure the degree of cure of thermoset resins through characterization of the changing viscoelasticity of a curing resin. By coupling a miniature actuator to a fiber optic strain sensor, the assembly can be made to vibrate while immersed in a curing resin. Comparison of the phase of the electrical actuation to the phase of the resulting strain in the sensor permits a measure of the loss tangent of the resin, where the loss tangent is the ratio of the loss modulus to the storage modulus. As the crosslinking of the resin proceeds, the loss tangent also changes, reflecting the changing rheology of the resin. The loss tangent is found to attain a maximum at the gel point of the resin, when a polymer network is formed. Further crosslinking may be tracked as the loss tangent decreases following gelation. After complete cure of the epoxy, the fiber optic sensor functions as a conventional optical strain sensor, permitting in-service strains in the composite part to be measured. Preliminary experimental results are presented here, which demonstrate that by combining a magnetostrictive actuator with a fiber optic strain sensor, the rheology of a curing thermoset resin may be monitored by measuring the changing loss tangent of the resin.