Magnetic spin and orbital moments of size-selected free iron cluster ions Fe{n}{+} (n=3-20) have been determined via x-ray magnetic circular dichroism spectroscopy. Iron atoms within the clusters exhibit ferromagnetic coupling except for Fe{13}{+}, where the central atom is coupled antiferromagnetically to the atoms in the surrounding shell. Even in very small clusters, the orbital magnetic moment is strongly quenched and reduced to 5%-25% of its atomic value while the spin magnetic moment remains at 60%-90%. This demonstrates that the formation of bonds quenches orbital angular momenta in homonuclear iron clusters already for coordination numbers much smaller than those of the bulk.