Asteroids with companions constitute an excellent sample for studying the collisional and dynamical evolution of minor planets. The currently known binary population were discovered by different complementary techniques that produce, for the moment, a strongly biased distribution, especially in a range of intermediate asteroid sizes (~20 to 100km) where both mutual photometric events and high-resolution adaptive optic imaging are poorly efficient. A totally independent technique of binary asteroid discovery, based on astrometry, can help to reveal new binary systems and populate a range of sizes and separations that remain nearly unexplored. In this work, we describe a dedicated period detection method and its results for the Gaia DR3 data set. This method looks for the presence of a periodic signature in the orbit post-fit residuals. After conservative filtering and validation based on statistical and physical criteria, we are able to present a first sample of astrometric binary candidates, to be confirmed by other observation techniques such as photometric light curves and stellar occultations.