This work presents a theoretical analysis of the generation of twisted terahertz (THz) radiation using laser-bunched relativistic electron beams in a magnetic wiggler. By employing a laser-bunched relativistic electron beam, which introduces a transverse modulation to the electron beam density, and a magnetic wiggler, which induces a transverse deflection to the electron trajectories, the generation of twisted THz radiation is achieved. The interaction between the modulated electron beam and the magnetic field leads to the emission of THz photons with a twisted phase structure. The findings of this study provide valuable insights into the generation and manipulation of twisted THz radiation contributing to the advancement of THz technology and its diverse applications.