[1] A Real Madrid youth graduate, he served three loan stints during his tenure, one in the lower leagues with CD Díter Zafra,[2] eventually making his debut for the former's first team on 14 October 1979 in a 3–2 home win against Real Zaragoza and scoring twice as a second-half substitute;[3] he could never impose himself in the capital side's main squad, however, totalling only 16 La Liga games from 1979 to 1981.

Rincón joined Andalusia's Real Betis for the 1981–82 season, netting 20 league goals in his second year which earned him the Pichichi Trophy, even though his team could only rank 11th.

His debut came on 27 April 1983 in a UEFA Euro 1984 qualifier against the Republic of Ireland, in Zaragoza; in only 15 minutes of play, after replacing FC Barcelona's Francisco Carrasco, he scored the final 2–0.

[11][12] On 21 December 1983, in his sixth international, Rincón netted four times in Spain's historic 12–1 victory over Malta, in a Euro 1984 qualifying match played in Seville.

[13] He would not be however picked for the finals in France, being selected two years later for the 1986 FIFA World Cup squad but making no appearances in Mexico.