This proceeding details the experimental investigation and scheme used to generate vortex beams at THz and far-infrared frequencies. Main experimental and numrical results are presented by M. Ivanov et al.<sup>1, 2</sup> We investigate the generation of broadband terahertz (THz) pulses between 10 and 40 THz with a phase singularity from two-color femtosecond laser-induced gas-plasmas. Experimental scheme allows for independent control of the amplitude, phase, polarization, and longitudinal and transverse positions of fundamental and second harmonics. When the second harmonic beam has a vortex charge the THz beam acquires an azimuthal phase modulation as well. Moreover, it turns out that also the THz intensity becomes modulated along the azimuthal angle. The phase structure of the singular THz beam is indirectly revealed by astigmatic transformation of the beam by a cylindrical mirror and additionally confirmed by the vortex THz beam behaviour upon change of relative phase between the fundamental and the second harmonic.