The magnetic propertiesof transition-metal ions aregenerallydescribed by the atomic spins of the ions and their exchange coupling.The orbital moment, usually largely quenched due the ligand field,is then seen as a perturbation. In such a scheme, S = 1/2 ions are predicted to be isotropic. We investigate a Co-(II)complex with two antiferromagnetically coupled 1/2 spins on Au(111)using low-temperature scanning tunneling microscopy, X-ray magneticcircular dichroism, and density functional theory. We find that eachof the Co ions has an orbital moment comparable to that of the spin,leading to magnetic anisotropy, with the spins preferentially orientedalong the Co-Co axis. The orbital moment and the associatedmagnetic anisotropy is tuned by varying the electronic coupling ofthe molecule to the substrate and the microscope tip. These findingsshow the need to consider the orbital moment even in systems withstrong ligand fields. As a consequence, the description of S = 1/2 ions becomes strongly modified, which have importantconsequences for these prototypical systems for quantum operations.