Nonlinear Cherenkov radiation is a phenomenon of light first observed in 1970, and could be manipulated by phase matching conditions. However, under a rotatory symmetry, the nonlinear Cherenkov radiation was still untouched, where the rotation parameters in optics will introduce an additional phase to the beam, change the phase velocity of the electromagnetic wave and lead to novel optical phenomena. Here, we introduce the rotation as a new freedom, and study the nonlinear Cherenkov radiation in optically rotatory crystals in theory. With a quartz crystal as the representative, we derive the theoretical variations, which show that the phase velocity of the crystal coupled wave was found to be accelerated or decelerated by the rotational angular velocity, corresponding to the change of the Cherenkov radiation angle. In addition, the variation on effective nonlinear coefficient of quartz crystals with rotational polarization direction is analyzed theoretically and used to simulate the Cherenkov ring distribution in rotatory nonlinear optics. This work introduces the rotation parameter into the non-collinear phase matching process for the first time and may inspire the development of modern photonics and physics in rotatory fames.