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. Threedimensional "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.The generation of a quasi-static magnetic field in the laser-plasma interaction is a subject of many theoretical [1-10] and experimental studies [11][12][13]. Two approaches are considered: one consists in designing the target in such way that the interaction with the laser generates controlled azimuthal currents [7,8], another one proposes to transfer angular momentum from laser to electrons by using circularly polarized laser beam [1][2][3][4][5][6][11][12][13] or laser beam with a structured spatial shape [9,10]. In [1-6], the authors consider theoretically the magnetization of a medium exposed to a circularly polarized Gaussian laser beam. Plasma magnetization originates from the inverse Faraday effect, where the spin angular momentum of a laser beam is transfered to the plasma electrons due to dissipation processes such as collisions, ionization or radiation friction. This laser to electron angular momentum transfer has been experimentally observed [11][12][13]. Ali et al. [9], consider a linearly polarized laser beam carrying Orbital Angular Momentum (OAM) [14] and analytically demonstrate that such a laser beam transfers its OAM to electron through the inverse bremsstrahlung dissipative process. Lécz et al. [10] and Wang et al.[15] numerically model the interaction of a screw-shaped laser pulse with an underdense plasma and observe laser to electron OAM transfer in the laser wakefield.In this letter, we demonstrate that a quasi-static axial magnetic field can be generated within a purely optical process, without any dissipative effects. It is produced in an underdense plasma irradiated by a radially polarized OAM laser beam, which is for example, experimentally designed by Li et al. [16]. The authors demonstrate their capacity to produce such laser beams with an energy ratio between radial and azimuthal components attaining 98%. Our three-dimensional (3D) Particle In Cell (PIC) simulations, modeling the laser-plasma interaction, clearly show an orbital angular momentum trans-fer from laser to electron and the generation of a strong solenoidal magnetic field. A simplified model describing the laser-electron dynamics shows that this transfer originates from the joint radial and longitudinal electron motion in the la...