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An Acousto-Optic Gyroscope (AOG) consisting of a Mach-Zehnder interferometer (MZI) embedded into two inherently matched piezoelectric SAW resonators sharing the same cavity is presented. This constitutes the first demonstration of a MEMS strain-based optomechanical gyroscope that uses refractive index change due to the acousto-optic effect rather than conventional displacement sensing. This first prototype integrates acoustic and photonic components on the same lithium niobate on insulator (LNOI) substrate and showcases how optical detection can provide greater stability compared to acousto-electric transduction. This approach enables the development of a new class of MEMS-based gyroscopes that combines the advantages of both conventional MEMS and optical gyroscopes.