In the 5d layered perovskite material, Sr2IrO4, spin orbit coupling and strong electron correlations combine to give rise to a spin-orbit coupled Mott insulator, with a pseudo-spin J=1/2 antiferromagnetic ground state. Recently, optical second-harmonic generation measurements and polarized neutron diffraction in Rh doped Sr2IrO4 have highlighted an odd-parity hidden order developing prior to its antiferromagnetic state. This state possesses the same symmetries of a loop-current order, theoretically proposed to account for the pseudo-gap physics of superconducting cuprates. The aim of this proposal is to detect the tiny orbital moments associated with these current loops using the exquisite sensitivity of muSR in order to unravel the nature of the hidden order in these iridate materials.