The search for periodic signals from blazars has become a widely discussed topic in recent years. In the scenario that such periodic changes originate from the innermost regions of blazars, the signals bear imprints of the processes occurring near the central engine, which are mostly inaccessible to our direct view. Such signals provide insights into various aspect of blazar studies, including disk-jet connection, magnetic-field configuration and, more importantly, strong gravity near the supermassive black holes and release of gravitational waves from binary supermassive-black-hole systems. In this work, we report the detection of a periodic signal in the radio light curve of blazar J1043+2408 spanning ∼10.5 years. We performed multiple methods of time-series analysis, namely, epoch folding, Lomb–Scargle periodogram, and discrete autocorrelation function. All three methods consistently revealed a repeating signal with a periodicity of ∼560 days. To robustly account for the red-noise processes usually dominant in the blazar variability and other possible artefacts, a large number of Monte Carlo simulations were performed. This allowed us to estimate high significance (99.9% local and 99.4% global) against possible spurious detection. As possible explanations, we discuss a number of scenarios, including binary supermassive-black-hole systems, Lense–Thirring precession, and jet precession.