In this Letter, we investigate a magnetic field induced by guiding plasmonic modes in graphene-coated nanowire via an inverse Faraday effect. Magnetic field distribution for different plasmonic modes has been calculated. It has been shown that a magnetic field has a vortex-like distribution for some plasmonic modes. The possibility of producing magnetic field distribution that rotates along the nanowire axis and periodically depends on azimuthal angle has been demonstrated.