The relationship between indirect exchange coupling and interlayer d-electron magnetic moments is studied using magnetometry and x-ray magnetic circular dichroism (XMCD) in Fe/Cr multilayers. Multilayers are simultaneously prepared with growth axes along different crystallographic orientations to determine the orientation dependence of these properties. We find the Cr moments are antiparallel to the Fe, and that a Cr thickness (${\mathrm{t}}_{\mathrm{Cr}}$) of 1 ML has a moment of \ensuremath{\approx}-0.7${\mathrm{\ensuremath{\mu}}}_{\mathrm{B}}$, 50% larger than the Cr moment developed in Fe-based dilute Cr alloys. For larger ${\mathrm{t}}_{\mathrm{Cr}}$ the Cr moment decays very quickly with distance from the Fe interface, while the Fe moment remains bulklike at all Cr thicknesses. It is found that for ${\mathrm{t}}_{\mathrm{Cr}}$10 \AA{} there are slight differences in the indirect (oscillatory) exchange coupling between Fe layers depending on crystallographic orientation. Intuitively, one would also expect an orientation dependence to the induced Cr moments, but we find them to be orientation independent. The orientation independence of the Cr moments correlates well with the orientation independent coupling which has been previously observed for ${\mathrm{t}}_{\mathrm{Cr}}$g10 \AA{}.