We present rotation period measurements for 107 M dwarfs in the mass range $0.15-0.70 M_\odot$ observed within the context of the APACHE photometric survey. We measure rotation periods in the range 0.5-190 days, with the distribution peaking at $\sim$ 30 days. We revise the stellar masses and radii for our sample of rotators by exploiting the Gaia DR2 data. For $\sim 20\%$ of the sample, we compare the photometric rotation periods with those derived from different spectroscopic indicators, finding good correspondence in most cases. We compare our rotation periods distribution to the one obtained by the Kepler survey in the same mass range, and to that derived by the MEarth survey for stars in the mass range $0.07-0.25 M_\odot$. The APACHE and Kepler periods distributions are in good agreement, confirming the reliability of our results, while the APACHE distribution is consistent with the MEarth result only for the older/slow rotators, and in the overlapping mass range of the two surveys. Combining the APACHE/Kepler distribution with the MEarth distribution, we highlight that the rotation period increases with decreasing stellar mass, in agreement with previous work. Our findings also suggest that the spin-down time scale, from fast to slow rotators, changes crossing the fully convective limit at $\approx0.3 M_\odot$ for M dwarfs. The catalogue of 107 rotating M dwarfs presented here is particularly timely, as the stars are prime targets for the potential identification of transiting small planets with TESS and amenable to high-precision mass determination and further atmospheric characterization measurements.
