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The bright blazar OJ 287 is the best-known candidate for hosting a supermassive black hole binary system. It inspirals due to the emission of nanohertz gravitational waves (GWs). Observations of historical and predicted quasi-periodic high-brightness flares in its century-long optical lightcurve, allow us to determine the orbital parameters associated with the binary black hole (BBH) central engine. In contrast, the radio jet of OJ 287 has been covered with Very Long Baseline Interferometry (VLBI) observations for only about 30 yr and these observations reveal that the position angle (PA) of the jet exhibits temporal variations at both millimetre and centimetre wavelengths. Here, we associate the observed PA variations in OJ 287 with the precession of its radio jet. In our model, the evolution of the jet direction can be associated either with the primary black hole (BH) spin evolution or with the precession of the angular momentum direction of the inner region of the accretion disc. Our Bayesian analysis shows that the BBH central engine model, primarily developed from optical observations, can also broadly explain the observed temporal variations in the radio jet of OJ 287 at frequencies of 86, 43, and 15 GHz. Ongoing Global mm-VLBI Array (GMVA) observations of OJ 287 have the potential to verify our predictions for the evolution of its 86-GHz PA values. Additionally, thanks to the extremely high angular resolution that the Event Horizon Telescope (EHT) can provide, we explore the possibility to test our BBH model through the detection of the jet in the secondary BH. © 2021 The Author(s)., This research has made use of data from the MOJAVE database that is maintained by the MOJAVE team Lister et al (2018). LD thanks FINCA and acknowledges the hospitality of University of Turku. LD, AG, and AS acknowledge the support of the Department of Atomic Energy, Government of India, under Project Identification no. RTI 4002. JLG and RL acknowledges the support of the Spanish Ministerio de Economía y Competitividad (grantsAYA2016-80889-P, PID2019-108995GB-C21), the Consejería de Economía, Conocimiento, Empresas y Universidad of the Junta de Andalucía (grant P18-FR-1769), the Consejo Superior de Investigaciones Científicas (grant 2019AEP112), and the State Agency for Research of the Spanish MCIU through the ‘Center of Excellence Severo Ochoa’ award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709).