During his career the forward played solely for Athletic Bilbao, in a professional spell which spanned nearly 20 years. He was one of the club's most iconic players, and later also worked as a coach with the team.
Born in Bilbao, Biscay, Rojo joined local giants Athletic Bilbao's youth ranks at an early age. In 1965 he started playing for its reserves but, after only three appearances, was promoted to the first team, and stayed there until his professional retirement 17 years later.
Rojo made his La Liga debut on 26 September 1965 in a 0–1 away loss against Córdoba CF, and helped Athletic to two Copa del Rey trophies. He played a total of 414 games in the Spanish top flight, becoming the player with the second-most appearances in the Basque side's history, only behind José Ángel Iribar; for several seasons he shared teams with younger brother José Ángel, with the pair being thus referred to as 'Rojo I' and 'Rojo II'.
In 1982, aged 35, Rojo retired as a footballer and began a coaching career – a testimonial match was held in his honour, with Athletic Bilbao hosting the England national team. His first managerial experience would be with the former's reserves, and he was promoted to first-team duties early into the 1989–90 campaign, being sacked at its closure.
After a four-year spell at Celta de Vigo, achieving promotion to the top level in his second season, Rojo returned to the second division for the next three years, coaching CA Osasuna and UE Lleida. For 1997–98 he was appointed at UD Salamanca, helping the modest club retain its first division status, and the following season he joined Real Zaragoza, leading them to the fourth place in 2000 – with the team failing to qualify for the UEFA Champions League only because the fifth-placed side, Real Madrid, won the campaign's most important European trophy – which earned him a return to Athletic.