The generation of vortex terahertz (THz) radiation by the interaction of a two-color Laguerre–Gaussian (LG) laser with plasmas under an external magnetic field is investigated theoretically and numerically. It is found that the vortex THz radiation with good monoenergetic properties can be generated successfully, and the orbital angular momentum of the LG lasers can be transferred to the radiation. In this scheme, the external magnetic field can not only enhance the intensity but can also break the spatial distribution symmetry of the vortex THz radiation. With the increase in the initial plasma density, the intensity of the vortex THz radiation increases significantly before reaching saturation and the spatial period of the radiation decreases, which indicates the monoenergetic peak of the vortex THz radiation can be well controlled through the initial plasma density. The relevant conclusions are verified by two-dimensional particle-in-cell simulations.