We use a low-temperature scanning tunneling microscope to study the interplay between the Kondo effect of a single-atom contact and a spin current. To this end, a nickel tip is coated by a thick layer of copper and brought into contact with a single Co atom adsorbed on a Cu(100) surface. We show that upon contact the Kondo resonance of Co is spin split and attribute the splitting to the spin current produced by the nickel tip and flowing across the copper spacer. A quantitative line shape analysis indicates that the spin polarization of the junction amounts up to 18%, but decreases when a pristine nickel tip is directly contacted to the Co atom.