A material extrusion (MEX) technology has been developed for the additive manufacturing of continuous carbon fiber–reinforced silicon carbide ceramic (Cf/SiC) composites. By comparing and analyzing the rheological properties of the slurries with different compositions, a slurry with a high solid loading of 48.1 vol% and high viscosity was proposed. Furthermore, several complex structures of Cf/SiC ceramic composites were printed by this MEX additive manufacturing technique. Phenolic resin impregnation–carbonization process reduces the apparent porosity of the green body and protects the Cf. Finally, the reactive melting infiltration (RMI) process was used to prepare samples with different Cf contents from 0 to 2 K (a bundle of carbon fibers consisting of 1000 fibers). Samples with Cf content of 1 K show the highest bending strength (161.6 ± 10.5 MPa) and fracture toughness (3.72 ± 0.11 MPa·m1/2) while the thermal conductivity of the samples with the Cf content of 1 K reached 11.0 W/(m·K). This study provides a strategy to prepare Cf/SiC composites via MEX additive manufacturing and RMI.