After starting his career at CD Getxo, the 19-year-old signed with Basque club Athletic Bilbao, making his La Liga debut on 31 December 1950 in a 2–0 away loss against Atlético Madrid in what would be his only appearance of the season.
After a loan to Barakaldo CF in the same region, in the second division, Orúe returned to Athletic to be an instrumental part of the sides that won one league and three Copa del Rey trophies in the 50s, including the double in the 1955–56 campaign, with the player contributing with 35 official games (one goal, in a 3–2 home win against Deportivo Alavés on 1 January 1956, his only as a professional).
Part of the team that was dubbed "The 11 villagers"[1]– which also included the likes of Canito, Carmelo Cedrún, Jesús Garay and José María Maguregui – Orúe left Bilbao after 1967–68 at the age of 37.
He appeared in 391 league matches for his main club, fourth-most after José Ángel Iribar, Joseba Etxeberria and Txetxu Rojo (480 overall).
Orúe's other two appearances arrived in 1957, against Holland (5–1 win, friendly) and Switzerland (2–2, in a 1958 FIFA World Cup qualifier).