Context. The search for periodic features in flux variability and kinematics of superluminal components in blazars is capable of providing significant clues for the understanding of the physical processes in their central engines (black-hole/accretion-disk systems), especially concerning the formation and structure of their relativistic jets and radiation mechanisms. Aims. The jet swing on parsec-scales and the change of the ejection position angle of the superluminal components with time in the quasar B1308+326 (z = 0.997) are investigated as quasi-periodic behaviors. Methods. A previously published precessing jet nozzle model is applied to model the source kinematics and a possible jet precession period is found. Results. Based on the model fitting of the kinematics for a subset of components, it is shown that their kinematics, including the shape of the inner trajectories and the motion of the components, could be well fitted in terms of the precessing jet nozzle model and a precession period of ~16.9 ± 0.3 yr is derived. Different precession mechanisms are discussed and compared. Conclusions. It is shown that the swing of the ejection position angle of the superluminal knots observed in B1308+326 may be due to the orbital motion of a putative supermassive black hole binary in its nucleus. Some relevant parameters of the binary model are estimated. We also discuss the spin-induced precession mechanism in the single black hole scenario and an estimate for the spin of the Kerr black hole is obtained.