We demonstrate the electrical beat note analysis and radio frequency (RF) injection locking of a continuous wave (cw) terahertz quantum cascade laser (QCL) emitting around 3 THz (～100 μm). In free running the beat note frequency of the QCL shows a shift of ～180 MHz with increasing drive current. The beat note, modulation response, injection pulling, and terahertz emission spectral characteristics in the different current regimes I, II, and III are investigated. The results show that in the current regime I close to the laser threshold we obtain a narrower beat note and flat response to the RF modulation at the cavity round trip frequency. The pulling effect and spectral modulation measurements verify that in the current regime I the RF injection locking is more efficient and a robust tool to modulate the mode number and mode frequency of terahertz QCLs.