The concept of crystalline disclinations in solid-state physics has gained attention in recent years, particularly with a focus on two-dimensional ${C}_{n}$-symmetric topological crystalline insulators. Research in this area has revealed novel topological phases different from the traditional bulk-boundary correspondence, expanding the topological material family. However, there remains a need to investigate the bulk-disclination correspondence in three-dimensional topological semimetals. We present an example of a higher-order Dirac semimetal in acoustic crystals with central disclinations. Our simple model not only exhibits hinge modes in the vertical direction but also supports a robust one-dimensional disclination hinge state along the central bulk-hollow path. Simulations demonstrate that our structure is capable of realizing backscatter-free disclination and higher-order hinge waves under the same architecture. Our findings offer insight for potential applications in acoustic devices for sound wave propagation and manipulation, as well as for exploring more exotic high-performance three-dimensional acoustic metamaterials.