Spherical-top tetrahedral species like CH4, SiH4, CF4,… possess no permanent dipole moment. Therefore, probing their pure rotation spectrum is very challenging since only a very weak dipole moment can be induced by centrifugal distortion and/or rovibrational interaction. If some Q branch lines have been recorded thanks to microwave techniques, R branch lines in the THz region have been poorly explored until recently. In previous studies, we have reported the pure rotation THz spectrum of cold and hot band lines of methane recorded at the SOLEIL Synchrotron facility. Here, we present the first recorded THz spectrum of the R branch of CF4, a powerful greenhouse gas, in its $v_3=1$ state. This Fourier transform spectrum covers the R(20) to R(37) line clusters, in the 20-37 cm-1 spectral range. It was recorded thanks to a 150 m multiple path cell at room temperature. We could estimate the vibration-induced dipole moment value and also include the recorded line positions in a global fit of many CF4 transitions.