  We use single-crystal neutron diffraction to determine the crystal structure
symmetry and the magnetic evolution in the rhodium doped iridates $\rm
Sr_2Ir_{1-x}Rh_{x}O_4$ ($0\leq x \leq 0.16$). Throughout this doping range, the
crystal structure retains a tetragonal symmetry (space group $I4_1/a$) with two
distinct magnetic Ir sites in the unit cell forming staggered $\rm IrO_6$
rotation. Upon Rh doping, the magnetic order is suppressed and the magnetic
moment of Ir$^{4+}$ is reduced from 0.21 $\rm \mu_B$/Ir for $x=0$ to 0.18 $\rm
\mu_B$/Ir for $x=0.12$. The magnetic structure at $x=0.12$ is different from
that of the parent compound while the moments remain in the basal plane.
