Galaxy clusters are the largest structures for which there is observational evidence of a magnetized medium. Central cores seem to host strong magnetic fields ranging from a few 0.1 μG up to several 10 μG in cooling flow clusters. Numerous clusters harbour central powerful active galactic nuclei (AGN), which are thought to prevent cooling flows in some clusters. The influence of such feedback on the magnetic field remains unclear: does the AGN-induced turbulence compensate for the loss of magnetic amplification within a cool core? And how is this turbulence sustained over several Gyr? Using high-resolution magnetohydrodynamical simulations of the self-regulation of a radiative cooling cluster, we study for the first time the evolution of the magnetic field within the central core in the presence of a powerful AGN jet. It appears that the jet-induced turbulence strongly amplifies the magnetic amplitude in the core beyond the degree to which it would be amplified by pure compression in the gravitational field of the cluster. The AGN produces a non-cooling core and increases the magnetic field amplitude in good agreement with μG field observations.