A tens of Tesla quasi-static axial magnetic field can be produced in the interaction of a short intense laser beam carrying an Orbital Angular Momentum with an underdense plasma. Three-dimensional "Particle In Cell" simulations and analytical model demonstrate that orbital angular momentum is transfered from a tightly focused radially polarized laser beam to electrons without any dissipative effect. A theoretical model describing the balistic interaction of electrons with laser shows that particles gain angular velocity during their radial and longitudinal drift in the laser field. The agreement between PIC simulations and the simplified model identifies routes to increase the intensity of the solenoidal magnetic field by controlling the orbital angular momentum and/or the energy of the laser beam.