We demonstrate the operation of a rotation sensor based on the nitrogen-14 (14N) nuclear spins intrinsic to nitrogen-vacancy (NV) color centers in diamond. The sensor uses optical polarization and readout of the nuclei and a radio-frequency double-quantum pulse protocol that monitors 14N nuclear spin precession. This measurement protocol suppresses the sensitivity to temperature variations in the 14N quadrupole splitting, and it does not require microwave pulses resonant with the NV electron spin transitions. The device was tested on a rotation platform and demonstrated a sensitivity of 4.7°/ (13 mHz/), with a bias stability of 0.4 °/s (1.1 mHz).