We report the magnetic structure of nominally 10% Cd-doped CeIrIn$_5$, CeIr(In$_{0.9}$Cd$_{0.1}$)$_5$, determined by elastic neutron scattering. Magnetic intensity was observed only at the ordering wave vector $Q_{AF} = (1/2,1/2,1/2)$, commensurate with the crystal lattice. A staggered moment of 0.47(3)$mu_B$ at 1.8 K resides on the Ce ion. The magnetic moments are found to be aligned along the crystallographic $c$ axis. This is further confirmed by magnetic susceptibility data, which suggest the $c$ axis to be the easy magnetic axis. The determined magnetic structure is strikingly different from the incommensurate antiferromagnetic ordering of the closely related compound CeRhIn$_5$, in which the magnetic moments are antiferromagnetically aligned within the tetragonal basal plane.