Moiré quasicrystals, formed by stacking periodic structures with a relative twist between them, exhibit many exotic phenomena. Their quasiperiodicity leads to effects such as light localization-delocalization transitions, superconductivity, topological states, and quasiband dispersion. However, weak interlayer interactions, the scalar nature of acoustic fields, and longer wavelengths severely limit the demonstration of these phenomena in acoustics. Here, we report an acoustic moiré quasicrystal that not only achieves a localization-delocalization transition, but also enables wave propagation shifting from diffusion to canalization or localization as a function of the quasicrystal geometry. Unlike conventional two-dimensional materials, the designed sublattice provides tailorable anisotropy and spatial broken symmetry, allowing quasicrystal structures to exhibit reconfigurable nontrivial dispersion. Furthermore, by introducing a uniform tilt angle in the unit cells breaks the spatial symmetry of the moiré quasicrystal, resulting in partial attenuation and disappearance of the wave within the localization pattern. Our findings pave a new avenue for controlling the properties of acoustic wave patterns, and benefit potential applications in energy transfer, subwavelength wave propagation, and highly sensitive sensors.