We examine the clustering properties of low–power radio galaxies at redshift 0.4 < z < 0.8 , using data from the 2SLAQ Luminous Red Galaxy ( LRG ) survey , and find that radio–detected LRGs ( with typical optical luminosities of 3 - 5 L _ { * } and 1.4 GHz radio powers in the range 10 ^ { 24 } to 10 ^ { 26 } W Hz ^ { -1 } ) are significantly more clustered than a matched population of radio–quiet ( \la 10 ^ { 24 } W Hz ^ { -1 } ) LRGs with the same distribution in optical luminosity and colour . The measured scale length of the two–point cross-correlation function between the full LRG sample and the radio–detected LRGs is 9.57 \pm 0.50 h ^ { -1 } Mpc , compared to 8.47 \pm 0.27 h ^ { -1 } Mpc for the matched sample of radio–quiet LRGs ; while the implied scale length of the auto-correlation function , r _ { 0 } , is 12.3 \pm 1.2 h ^ { -1 } Mpc and 9.02 \pm 0.52 h ^ { -1 } Mpc for the radio–detected and radio–quiet samples respectively . We further interpret our clustering measurements in the halo model framework and demonstrate that the radio–detected LRGs have typical halo masses of 10.1 \pm 1.4 \times 10 ^ { 13 } h ^ { -1 } M _ { \odot } and bias of 2.96 \pm 0.17 , compared to 6.44 \pm 0.32 \times 10 ^ { 13 } h ^ { -1 } M _ { \odot } and 2.49 \pm 0.02 for the radio–quiet sample . A model in which the radio–detected LRGs are almost all central galaxies within haloes provides the best fit to the measured clustering , and we estimate that at least 30 \% of all 2SLAQ LRGs with the same clustering amplitude as the radio–detected LRGs are currently radio–loud . Our results imply that radio–detected galaxies in the 2SLAQ LRG sample typically occupy more massive haloes than other LRGS of the same optical luminosity , so the probability of finding a radio–loud AGN in a massive galaxy at z \sim 0.55 is influenced by the halo mass and/or cluster environment in addition to the well-known dependence on optical luminosity . If we model the radio–detected fraction of LRGs , F _ { rad } , as a function of halo mass M , then the data are well-fitted by a power law of the form F _ { rad } \propto { M } ^ { 0.65 \pm 0.23 } . The observed relationship between radio emission and clustering strength could plausibly arise either through a higher fuelling rate of gas onto the central black holes of galaxies in the most massive haloes ( producing more powerful radio jets ) or through the presence of a denser IGM ( which would provide a more efficient working surface for the jets , thus boosting their observed radio luminosity ) . Further work is needed to determine which of these effects is dominant .