Today, the task of developing microoptical gyroscopes is topical. Usually, tunable lasers with a built-in frequency stabilization system are used in such gyroscopes. They are comparatively bulky, which hinders the real miniaturization of optical gyroscopes. We propose a new approach implemented by using a Mach–Zehnder modulator with a passive ring resonator connected to one of its arms. This makes it possible to obtain a mutual configuration and makes the use of a tunable laser optional. Two ring resonators made of the polarization-maintaining fiber, suitable for use as sensitive elements of a gyroscope, were realized and investigated. Their Q-factor is equal to 14.5 × 106 and 28.9 × 106. The maximum sensitivity of the proposed method when using the described resonators is 3.2 and 1.8 °/h, respectively. The first experimental setup of a resonator gyroscope implementing this approach has been manufactured and analyzed. When measuring the rotation speed by the quasi-harmonic signal span and its phase, the measurement accuracy was approximately 11 and 0.4 °/s, respectively.