  The ratio of orbital (L) and spin (S) contributions to the magnetically
ordered moments of a 5d transition metal oxide, Sr2IrO4 was evaluated by
non-resonant magnetic x-ray diffraction. We applied a new experimental setting
to minimize the error in which we varied only the linear-polarization of
incident x-ray at a fixed scattering angle. Strong polarization dependence of
the intensity of magnetic diffraction was observed, from which we conclude that
the ordered moments contain substantial contribution from the orbital degree of
freedom with the ratio of <L>/<S> ~5.0, evidencing the pronounce effect of
spin-orbit coupling. The obtained ratio is close to but slightly larger than
the expected value for the ideal J_eff = 1/2 moment of a spin-orbital Mott
insulator, |<J_1/2|L_z|J_1/2>|/|<J_1/2|S_z|J_1/2>| = 4, which cannot be
accounted by the redistribution of orbital components within the t_2g bands
associated with the elongation of the IrO6 octahedra.
