  The recent discovery of a roughly simultaneous periodic variability in the
light curves of the BL Lac 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 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 $2.24\pm0.03$ years, compatible with the periodicity
detected in the light curves of 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 PG 1553+113. We estimated the characteristics of this putative binary system
that also would be responsible for driving the inferred jet precession.
