The ratio of orbital (L) and spin (S) contributions to the magnetically ordered moments of a 5d transition metal oxide, Sr_{2}IrO_{4} was evaluated by nonresonant magnetic x-ray diffraction. We applied an improved experimental setting that minimized the experimental 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 pronounced 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 for by the redistribution of orbital components within the t_{2g} bands associated with the elongation of the IrO_{6} octahedra.