In this study, the joining of silicon carbide (SiC) ceramics was achieved via a Si–C reaction bonding method using the phenolic resin (PF)–MgCl2 system as the carbon precursor. Specifically, by adding MgCl2 to the phenolic resin mixture, the average pore size of the product of carbonization of the PF resin mixture increased from 14 ± 5 nm to 524 ± 21 nm, which was beneficial for the infiltration of molten silicon at high temperature. The microstructure of the joined specimens and the effect of the inert filler on the joint strength were investigated. It was demonstrated that SiC–SiC joints with strong interfacial bonding and high flexural strength could be obtained by the Si–C reaction bonding method using a phenol formaldehyde resin/alcohol sol-gel system as the carbon precursor. The flexural strength of the joined specimens reached the highest value, i.e., 308 ± 27 MPa when the solid loading of the inert filler was 26%. Overall, stable joining of silicon carbide ceramics was achieved by the proposed method, which has significance for realizing the preparation of complex-shaped or large silicon carbide ceramic parts.