  We propose a scheme to realize the rotation sensing using optical lattices
with laser-assisted tunneling. We demonstrate that the competition between the
rotation and the spin-orbit coupling governs the spin-dependent response of the
cyclotron dynamics of the spin-orbit coupled bosons. The Sagnac-type cumulative
phase can be read out from the envelop of a beat-frequency particle current in
the spin-balanced system and enhanced by the cyclotron motion. We also
theoretically show that the sensitivity limit of the spin-orbit-coupled system
to the rotational motion can reach 7*10^-8 rad s^-1 Hz^1/2.
