Drescher took part in the first official Danish national team game, played at the 1908 Summer Olympics. He was the starting goalkeeper in all three Danish games at the 1908 Olympic football tournament, as Denmark won silver medals. He played his fourth and last Danish national team game in May 1910. Drescher was once again selected for the Danish squad at the 1912 Summer Olympics. He was an unused reserve player throughout the games, and did not receive a medal, as Denmark won silver again in the 1912 Olympic football tournament.