MAORY (Multi-conjugate Adaptive Optics RelaY) and MICADO (MCAO Imaging CamerA for Deep Observations) will perform the science in the Multi-conjugate Adaptive Optics mode of the ELT (Extremely Large Telescope). One of their goals is the multi-object differential astrometry which requires low optical distortion and diffraction limited aberrations. To align MAORY, an automate method will be used during the integration of the instrument and could be part of the calibration strategy at the ELT site. This paper describes the method and the ray-tracing simulations carried out to validate the algorithm. Even in presence of different error sources, the method works in a large range of misalignments bringing the system close to the nominal performances.