 Having won slightly more than 20 caps for Spain, Rincón appeared with the national team at the 1986 World Cup.Rincón was born in Lavapiés, Madrid.A Real Madrid youth graduate, he served three loan stints during his tenure, one in the lower leagues with CD Díter Zafra, eventually making his debut for the first team on 14 October 1979 in a 3–2 home win against Real Zaragoza and scoring twice as a second-half substitute; he could never impose himself in the capital side's main squad, however, amassing only 16 La Liga games from 1979 to 1981.