We have determined the magnetic properties of single-crystalline Au nanorods in solution using an optically detected magnetic alignment technique. The rods exhibit a large anisotropy in the magnetic volume susceptibility (Δχ(V)). Δχ(V) increases with decreasing rod size and increasing aspect ratio and corresponds to an average volume susceptibility (χ(V)), which is drastically enhanced relative to bulk Au. This high value of χ(V) is confirmed by SQUID magnetometry and is temperature independent (between 5 and 300 K). Given this peculiar size, shape, and temperature dependence, we speculate that the enhanced χ(V) is the result of orbital magnetism due to mesoscopic electron trajectories within the nanorods.