Born in Bilbao, Biscay, Rojo joined the youth system of hometown club Athletic Bilbao in his last year as a junior. He made his senior debut with neighbouring SD Indautxu, being loaned twice to the Segunda División team and being relegated as many times; he also played in this competition with the former's reserves, again dropping down a level in the 1969–70 season after losing a play-off against Villarreal CF. Aged 22, Rojo was definitely promoted to the first team before the start of the following campaign. By that time his elder brother José Francisco was already an established member of the line-up, and therefore the younger sibling was usually referred to administratively as Rojo II. José Ángel made his debut in La Liga on 24 January 1971 when he came on as a late substitute in a 2–1 away victory against Real Zaragoza, and he went on to start six further league games for Ronnie Allen's team, adding four appearances in the Copa del Generalísimo. In 1971–72 Rojo began to feature regularly for Athletic, and made his European debut against Southampton, featuring the full 90 minutes in the 1–2 away loss in the UEFA Cup. The following season he contributed with 37 appearances in all competitions, helping the side to ninth place in the league and victory in the domestic cup, with the player appearing in the final in Madrid, a 2–0 defeat of CD Castellón. Over the next four campaigns, Rojo was a frequent presence in the midfield for Athletic. In 1976, he was in the side and scored in both legs of a Spanish Cup tie against Sporting de Gijón in which the opponents overturned a 2–0 first leg deficit to win 5–2 at San Mamés. Although the result itself was an embarrassment, it did prompt the club to pursue the opposition's star player :es:José Ignacio Churruca|Iñaki Churruca, who would play an important role for the team in the coming years. Rojo missed the first half of 1976–77 due to injury, scoring what was to be his final goal for the side in a 3–0 home win over Hércules CF as they ended the league in third place. Athletic also reached the final of the UEFA Cup, losing on the away goals rule to Juventus F.C. and with him appearing in the first leg, one of his five games in the run; he departed from Bilbao at the age of 29, with overall totals of 186 matches and 12 goals.
Having never featured at any youth level for Spain, Rojo came to the attention of the selectors due to his form for Athletic. His first and only cap arrived on 17 October 1973, when he played the entirety of a 0–0 friendly draw in Turkey – his brother also took part in the match. Previously, Rojo featured for the unofficial Basque Country team in 1971 in a match against Catalonia.
