*Club domestic league appearances and goals, correct as of 17:50, 18 October 2024 (UTC) ‡ National team caps and goals, correct as of 17:50, 18 October 2024 (UTC)
He played his first match in a friendly against Chile on 9 November 2016, but was substituted in the 15th minute with his team going on to lose 1–0. The same sides faced again on 11 November with Vargas playing the whole game as Ecuador lost 2–0.
Vargas was called up to the Ecuador squad for the 2017 South American U-20 Championship on home soil. In the tournament he only played once, being sent off for a second yellow card in the 46th minute in the 1–0 loss against Brazil. He did not feature again as Ecuador eventually ended as runners-up, losing the final 2–1 to Uruguay.