The claw-pole-rotor shaft has a front end with a radially larger-sized section, two knurled regions known as crimping regions, intended to be assembled with the claw-pole rotor by local deformation of the material of the claw-pole rotor, and a centring region for centring the claw-pole rotor, the crimping regions being positioned on each side of the centring region while the centring region projects radially with respect to the crimping regions of the shaft, these themselves projecting radially with respect to the section of larger radial size at the front end of the shaft. The claw-pole rotor is characterized in that it is equipped with such a shaft while the rotary electrical machine is characterized in that it is equipped with such a rotor.