The Perseus galaxy cluster is known to present multiple and misaligned pairs of cavities seen in X-rays, as well as twisted kiloparsec-scale jets at radio wavelengths; both morphologies suggest that the AGN jet is subject to precession. In this work we performed 3D hydrodynamical simulations of the interaction between a precessing AGN jet and the warm intracluster medium plasma, which dynamics is coupled to a NFW dark matter gravitational potential. The AGN jet inflates cavities that become buoyantly unstable and rise up out of the cluster core. We found that under certain circumstances precession can originate multiple pairs of bubbles. For the physical conditions in the Perseus cluster, multiple pairs of bubbles are obtained for a jet precession opening angle > 40 degrees acting for at least three precession periods, reproducing well both radio and X-ray maps. Based on such conditions, assuming that the Bardeen-Peterson effect is dominant, we studied the evolution of the precession opening angle of this system. We were able to constrain the ratio between the accretion disc and black hole angular momenta as 0.7 - 1.4. We were also able to constrain the present precession angle to 30 - 40 degrees, as well as the approximate age of the inflated bubbles to 100 - 150 Myrs.