Since the discovery of antiferromagnetism, metallic oxide RuO_{2} has exhibited numerous intriguing spintronics properties such as the anomalous Hall effect and anisotropic spin splitting effect. However, the microscopic origin of its antiferromagnetism remains unclear. By investigating the spin splitting torque in RuO_{2}/Py, we found that metallic RuO_{2} exhibits a spatially periodic spin structure which interacts with the spin waves in Py through interfacial exchange coupling. The wavelength of such structure is evaluated within 14-20 nm depending on the temperature, which is evidence of an incommensurate spin density wave state in RuO_{2}. Our work not only provides a dynamics approach to characterize the antiferromagnetic ordering in RuO_{2}, but also offers fundamental insights into the spin current generation due to anisotropic spin splitting effect associated with spin density wave.