We examine the hypothesis that mergers and close encounters between galaxies can fuel active galactic nuclei (AGNs) by increasing the rate at which gas accretes toward the central black hole. We compare the clustering of galaxies around radio-loud AGNs with the clustering around a population of radio-quiet galaxies with similar masses, colors, and luminosities. Our catalog contains 2178 elliptical radio galaxies with flux densities greater than 2.8 mJy at 1.4 GHz from the Six Degree Field Galaxy Survey. We find tentative evidence that radio AGNs with more than 200 times the median radio power have, on average, more close (r < 160 kpc) companions than their radio-quiet counterparts, suggesting that mergers play a role in forming the most powerful radio galaxies. For ellipticals of fixed stellar mass, the radio power is neither a function of large-scale environment nor halo mass, consistent with the radio powers of ellipticals varying by orders of magnitude over billions of years.