The effects of pressure on the crystal structure of aurophilic tetragonal gold iodide have been studied by means of powder X-ray diffraction up to 13.5 GPa. We found evidence of the onset of a phase transition at 1.5 GPa that is more significant from 3.8 GPa. The low-and high-pressure phases coexist up to 10.7 GPa. Beyond 10.7 GPa, an irreversible process of amorphization takes place. We determined the axial and bulk compressibility of the ambient-pressure tetragonal phase of gold iodide up to 3.3 GPa. This is extremely compressible with a bulk modulus of 18.1(8) GPa, being as soft as a rare gas, molecular solids, or organometallic compounds. Moreover, its response to pressure is anisotropic.