We present a comparison of the spin parameter λR, measured in a region dominated by the galaxy disc, between 20 pairs of nearby (0.005 < z < 0.03) seemingly isolated twin galaxies differing in nuclear activity. We find that 80-82% of the active galaxies show higher values of λR than their corresponding non-active twin(s), indicating larger rotational support in the active galactic nuclei (AGN) discs. This result is driven by the 11 pairs of unbarred galaxies, for which 100% of the AGN show larger λR than their twins. These results can be explained by a more efficient angular momentum transfer from the inflowing gas to the disc baryonic matter in the case of the active galaxies. This gas inflow could have been induced by disc or bar instabilities, although we cannot rule out minor mergers if these are prevalent in our active galaxies. This result represents the first evidence of galaxy-scale differences between the dynamics of active and non-active isolated spiral galaxies of intermediate stellar masses in the Universe.