  A high-sensitivity gyroscope is vital for both investigation of the
fundamental physics and monitor of the subtle variation of Earth's behaviors.
However, it is challenge to realize a portable gyroscope with sensitivity
approaching a small fraction of the Earth's rotation rate. Here, we
theoretically propose a method for implementing a table-top gyroscope with
remarkably high sensitivity based on photon drag in a rotating dielectric
object. By inserting an $\text{Er}^{3+}$-doped glass rod in a Fabry-P\'{e}rot
optical cavity with only 20 cm length, we theoretically show that the giant
group refractive index and the narrowing cavity linewidth due to slow light can
essentially increase the nonreciprocal phase shift due to the photon drag to
achieve a rotation sensitivity of $26$ frad/s/$\sqrt{Hz}$. This work paves the
way to accurately detect tiny variations of the Earth's rotation rate and
orientation, and even can test the geodetic and frame-dragging effects
predicted by the general relativity with a small-volume equipment.
