ɑːsˈoːɹɪˌoʊ skˈoːɹd hɪz fˈɜːst ˌɪntɚnˈæʃənəl ɡˈoʊl ˌɔn sˈɛvən dʒuːlˈaɪ tˈuː θˈaʊzənd fˈoːɹ ɪn ɐ tˈuː tˈuː dɹˈɔː ɐɡˈɛnst jˈʊɹɹuːɡwˌaɪ ɪnðə tˈuː θˈaʊzənd fˈoːɹ kˈoʊpə æmˈeɪɹɪkə.
Osorio scored his first international goal on 7 July 2004 in a 2–2 draw against Uruguay in the 2004 Copa América.