Using x-ray absorption spectroscopy at the Rh-L_2,3, Co-L_2,3, and Fe-L_2,3 edges, we find a valence state of Co^2+/Rh^4+ in Ca3CoRhO6 and of Fe^3+/Rh^3+ in Ca3FeRhO6. X-ray magnetic circular dichroism spectroscopy at the Co-L_2,3 edge of Ca3CoRhO6 reveals a giant orbital moment of about 1.7mu_B, which can be attributed to the occupation of the minority-spin d_0d_2 orbital state of the high-spin Co^2+ (3d^7) ions in trigonal prismatic coordination. This active role of the spin-orbit coupling explains the strong magnetocrystalline anisotropy and Ising-like magnetism of Ca3CoRhO6.