Thin films of the ferromagnetic metal SrRuO3 (SRO) show a varying easy magnetization axis depending on the epitaxial strain and undergo a metal-to-insulator transition with decreasing film thickness. We have investigated the magnetic properties of SRO thin films with varying thicknesses fabricated on SrTiO3(001) substrates by soft x-ray magnetic circular dichroism (XMCD) at the Ru M2,3 edge. Results have shown that, with decreasing film thickness, the film changes from ferromagnetic to non-magnetic around 3monolayer thickness, consistent with previous magnetization and magneto-optical Kerr effect measurements. The orbital magnetic moment perpendicular to the film was found to be ~ 0.1{mu}B/Ru atom, and remained nearly unchanged with decreasing film thickness while the spin magnetic moment decreases. Mechanism for the formation of the orbital magnetic moment is discussed based on the electronic structure of the compressively strained SRO film.