It has been technically challenging to efficiently couple external radio frequency (RF) power to cylindrical dielectric-loaded accelerating (DLA) structures, especially when the DLA structure has a high dielectric constant. This article presents a novel design of matching section for coupling the RF power from a circular waveguide to an <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>-band DLA structure with a dielectric constant <inline-formula> <tex-math notation="LaTeX">$\varepsilon _{\text {r}}=16.66$ </tex-math></inline-formula> and a loss tangent <inline-formula> <tex-math notation="LaTeX">$\tan \delta =3.43\times {10}^{-5}$ </tex-math></inline-formula>. It consists of a compact dielectric disk with a width of 2.035 mm and a base angle of 60°, resulting in a broadband coupling at a low RF field, which has the potential to survive in the high-power environment. To prevent a sharp dielectric corner break, a 45° chamfer is also added. A microscale vacuum gap, caused by metallic clamping between the thin coating and the outer thick copper jacket, is also studied in detail. Through optimization, most of RF power is coupled into the DLA structure, with no enhancement of peak electromagnetic fields above those of the structure itself. Tolerance studies on the geometrical parameters and mechanical design of the full-assembly structure are also carried out as a reference for fabrication.