At Recreation Club, he stood out for his defensive skills, which earned him a move to Athletic Club in 1905, making his competitive debut on 11 April 1906, at the 1906 Copa del Rey, in a 2–1 win over Recreativo de Huelva, but he did not play in the final against Madrid FC, and without him, Athletic conceded 4 goals in a 1–4 loss. In 1907, the best players from Athletic and Unión Vizcaino came together to form Bizcaya, which was specially created to take part in the 1907 Copa del Rey, and Arzuaga was elected into the team, forming a defensive partnership with his former Recreation Club teammate, Alfonso Sena of Vizcaino, which played a very important role in helping Bizcaya reach the final, and this time he started and nearly kept a clean-sheet, but they lost to Madrid once again, courtesy of a late goal from Manuel Prast.
