We demonstrate operation of a rotation sensor based on the $^{14}$N nuclear spins intrinsic to nitrogen-vacancy (NV) color centers in diamond. The sensor employs optical polarization and readout of the nuclei and a radio-frequency double-quantum pulse protocol that monitors $^{14}$N nuclear spin precession. This measurement protocol suppresses the sensitivity to temperature variations in the $^{14}$N 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 $^{circ}/sqrt{rm{s}}$ (13 mHz/$sqrt{rm{Hz}}$), with bias stability of 0.4 $^{circ}$/s (1.1 mHz).
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