  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).
