The recent discovery of a roughly simultaneous periodic variability in the light curves of the BL Lac object \object PG 1553+113 at several electromagnetic bands represents the first case of such odd behavior reported in the literature . Motivated by this , we analyzed 15 GHz interferometric maps of the parsec-scale radio jet of \object PG 1553+113 to verify the presence of a possible counterpart of this periodic variability . We used the Cross-Entropy statistical technique to obtain the structural parameters of the Gaussian components present in the radio maps of this source . We kinematically identified seven jet components formed coincidentally with flare-like features seen in the \gamma -ray light curve . From the derived jet component positions in the sky plane and their kinematics ( ejection epochs , proper motions , and sky position angles ) , we modeled their temporal changes in terms of a relativistic jet that is steadily precessing in time . Our results indicate a precession period in the observer ’ s reference frame of 2.24 \pm 0.03 years , compatible with the periodicity detected in the light curves of \object PG 1553+113 . However , the maxima of the jet Doppler boosting factor are systematically delayed relative to the peaks of the main \gamma -ray flares . We propose two scenarios that could explain this delay , both based on the existence of a supermassive black hole binary system in \object PG 1553+113 . We estimated the characteristics of this putative binary system that also would be responsible for driving the inferred jet precession .