Recently, single-walled carbon nanotubes as well as graphene functionalized with azobenzene chromophores have drawn attention for applications in optoelectronics due to their ability to undergo cis-trans isomerization when exposed to light. The electronic properties of the nanocarbon materials at these unconventional interfaces can be tailored by gaining structural insight into the organic monolayers at the molecular level. In this work, we use polarization-dependent X-ray absorption spectroscopy to probe the orientation of three chromophores on graphene, all identical except for their terminal groups. All three terminal groups (methyl, nitro, and nitrite) are well-oriented, with a tilt angle of about 30 from the substrate for the shared azobenzene group. Density functional theory calculations are in good agreement with experimental results and give two similar, stable configurations for the orientation of these molecules on graphene.