We investigate the stellar kinematics and stellar populations of 58 radio-loud galaxies of intermediate luminosities ( L _ { 3 GHz } > 10 ^ { 23 } W Hz ^ { -1 } ) at 0.6 \textless z \textless 1 . This sample is constructed by cross-matching galaxies from the deep VLT/VIMOS LEGA-C spectroscopic survey with the VLA 3 GHz dataset . The LEGA-C continuum spectra reveal for the first time stellar velocity dispersions and age indicators of z \sim 1 radio galaxies . We find that z \sim 1 radio-loud AGN occur exclusively in predominantly old galaxies with high velocity dispersions : \sigma _ { * } > 175 km s ^ { -1 } , corresponding to black hole masses in excess of 10 ^ { 8 } M _ { \odot } . Furthermore , we confirm that at a fixed stellar mass the fraction of radio-loud AGN at z \sim 1 is 5 - 10 times higher than in the local universe , suggesting that quiescent , massive galaxies at z \sim 1 switch on as radio AGN on average once every Gyr . Our results strengthen the existing evidence for a link between high black-hole masses , radio loudness and quiescence at z \sim 1 .