Almost all inertial navigation systems rely on optical gyroscopes, operating on the Sagnac effect. Laser gyroscopes demonstrate high precision in demanding applications such as seismology and geodesy. Passive optical gyroscopes, typically fiber-optic gyroscopes (FOGs), are of particular interest due to the lack of the “lock-in” effect, which is the most detrimental effect in active laser systems. Still, the current data acquisition rate of modern FOGs cannot satisfy emerging applications, particularly for autonomous navigation. Herein, a novel interferometric FOG, based on the measurements of ultrashort pulse phase via the dispersive Fourier transformation, is presented, demonstrating the highest upto-date acquisition rate of 15 MHz. This setup is insensitive to the timing jitter and the fluctuations of the carrier-envelope phase of the pulses. The single-shot resolution of the phase retrieval is 7.3 mrad, which corresponds to a time shift of 8.7 attoseconds. As a confirmation of the high-speed performance, movements of a stepper motor are recorded with an angular velocity resolution of 0.33 mdeg s_1 and a bias instability of 0.06 deg h_1 at acquisition time of 17.07 ìs. The proposed method can facilitate various phase measurements at a high repetition rate and is not limited only to gyroscopic applications.