The development of next-generation high-performance polymer composites for advanced manufacturing demands rapid, versatile, and energy-efficient manufacturing strategies. This work presents a novel approach for the fabrication of frontally-polymerized continuous carbon fiber-reinforced thermoset tows. The proposed process combines the advantages of direct ink writing, pultrusion and frontal-polymerization to enable tow extrusion and consolidation, in-situ curing, and rapid manufacturing of free-standing composite members with reduced processing time, energy, and cost. In this process, a pre-impregnated fiber tow is extruded and then pulled through heated rollers to compact the tow, cure the resin, and form the composite. We investigate the effects of compaction, extrusion rate, and roller temperature on the cure kinetics, front location, fiber volume fraction, and thermo-mechanical properties of the resulting composites. A homogenized thermo-chemical model is developed to capture the effect of process parameters on heat transfer in the tow and curing of the resin, and is compared with experiments.