Terahertz (THz) wireless communications are commonly regarded as one of the key technologies of 6G communication. Combined with THz, the newly exploited physical layer transmission dimension orbital angular momentum (OAM) that multiplexes a set of orthogonal modes on the same frequency channel, can unleash its potential in achieving high spectrum efficiency. Currently, most of the research on radio OAM communications focus on the point-to-point scenario in microwave and millimeter-wave (mmWave) bands. In this paper, we propose a uniform circular array (UCA)-based THz multi-user OAM (MU-OAM) communication system including downlink and uplink transmission schemes that simplifies the signal detection to the despiralization and amplitude detection (AD). A salient feature of the proposed MU-OAM communication scheme is lower computational complexity than the traditional MU-MIMO scheme without sacrifacing bit error rate (BER) and achievable sum rate performances, which is validated by mathematical analysis and numerical simulations.