All-optical switching of magnetic materials is a potential method for realizing high-efficiency and high-speed data writing in spintronics devices. The current method, which utilizes two circular helicities of light to manipulate magnetic domains, is based on femtosecond pulsed lasers. In this study, we demonstrate a new all-optical switching method using a continuous-wave Laguerre-Gaussian beam (twisted light), which allows photons to carry orbital angular momentum with discrete levels, lℏ, to modify the magnetic anisotropy of an interlayer exchange coupling system. The easy axis of the heterojunction Pt(5 nm)/Co(1.2 nm)/Ru(1.4 nm)/Co(0.4 nm)/Pt(5 nm) on a SiO2/Si substrate dramatically changed after illuminating it with a laser beam carrying a sufficient quantum number of orbital angular momentum. Based on a simple numerical calculation, we deduced that the interaction between the dynamical phase rotation of the electric field and the metal surface could generate an in-plane circular current loop that consequently induces a perpendicular stray field to change the magnetic anisotropy. This finding paves the way for developments in the field of magnetic-based spintronics using light with orbital angular momentum.