Terahertz (THz) field excitation by a rotating relativistic electron beam in a magnetized plasma column is described using numerical analysis and particle-in-cell simulation. A rotating electron beam propagating through a cylindrical plasma column excites plasma wakefields. The plasma wakefields couple with the electron beam to excite transverse currents at THz frequency. As a result, the energy of the wakefield directly converts into the form of electromagnetic radiation in the THz range. The magnetic field supports the transverse modes via electron cyclotron resonance. The strength of the THz field is enhanced due to scattering of the spiralling electron beam on the plasma density perturbation. The THz field amplitude is controllable by the electron beam velocity and beam density. On increasing the beam current, the THz field is enhanced significantly. The analytical results are compared with particle-in-cell simulations and are found to be in reasonable agreement.