Context. The study of periodic (or quasi-periodic) variabilities in optical and radio bands and quasi-periodic radio-jet swings are important to further our understanding of the physical processes in blazars. Among these the correlation between the periodic or quasi-periodic phenomena in radio and optical bands is particularly significant, because it can provide unique information about the relativistic jets and central engines in the nuclei of blazars. Aims. We aim to investigate the possibility that the radio jet swing on parsec scales observed in PG 1302-102 (z = 0.278) is a quasi-periodic phenomenon and study its correlation with the periodic optical variability claimed in a recently published work, seeking evidence for a binary black hole system. Methods. The precessing jet-nozzle model proposed in our previous works was applied to simulate the kinematics of the superluminal components. It is shown that the inner-jet kinematic features can well be explained in terms of the precessing nozzle model. Results. Based on the model simulation (model fitting) of the inner kinematics for its six superluminal components, a precession period of ~5.1583 ± 0.5 yr is derived for the radio jet swing and the kinematics of all the six components are consistently interpreted. The similarity between the radio jet precession period and the optical period found in its optical light curve may be physically significant. Both periodic behaviors in radio and optical bands could be explained in terms of the orbital motion of a black hole binary, if the orbital plane makes large inclinations to the sky plane: the orbital motion of the primary hole produces the periodic jet swing and the orbital motion of the secondary hole produces the periodic optical variability as suggested in the literature. Thus the total mass and the mass ratio of the binary are estimated. Conclusions. Based on this analysis, we show that PG 1302-102 might have a supermassive black hole binary existing in its nucleus and it is starting to enter its inspiral phase of merging. Gravitational radiation would start to dominate the energy-momentum loss for its orbital shrinkage.