Modern fiber-optic gyroscopes are calibrated using the Earth's rotation or stepper motor actuated rotation tables. We investigated the angular velocity resolution of the Optolink SRS-1000 fiber-optic gyroscope using a piezo-activated rotation table down to angular velocity steps of 1 x 10(-7) rad s(-1) with an accuracy of 1.5 x 10(-8) rad s(-1). To our knowledge, these are the smallest velocity steps resolved and reported in the literature so far. Our results show that such a gyroscope may be also used for nanopositioning purposes in addition to its usual navigation application.