We present the results of a long-term periodicity search in a sample of γ-ray blazars within a multiwavelength context. These blazars have been selected from the Steward Observatory sample as part of its optical monitoring program between 2008 and 2018. We study 15 sources with a temporal coverage in their optical total and polarized emission sufficiently large (>9 yr) to perform a reliable long-term periodicity analysis. We collect data from several observatories to extend the coverage, enabling the search of longer periods. In addition, data are also gathered in the high-energy (E > 100 MeV) γ-ray band from the Fermi Large Area Telescope; and in the 15 GHz radio band from the Owens Valley Radio Observatory. We identify 5 promising candidates to host quasi-periodic emission, AO 0235+164, PKS 1222+216, Mrk 501, BL Lacertae, and 1ES 2344+514 with periods in one or more bands and statistical significances ~3σ after trial factor correction. AO 0235+164 shows a period of ~8.2 yr in the R band; PKS 1222+216 has a quasi-periodic modulation in its total and polarized optical emission of ~1.6 yr; Mrk 501 displays a ~5 yr quasi-periodicity in optical and radio wavelengths; BL Lacertae presents a period of ~1.8 yr in its polarized emission; and 1ES 2344 + 514 shows a hint of a ~5.5 yr period in its optical R band. We interpret these results in the framework of the most common models and scenarios, namely the presence of a binary supermassive black hole system; or geometrical effects like helical or precessing jets.