Born in Alagón, Zaragoza, Angoy was a product of FC Barcelona's youth ranks. He made his professional debut with CD Logroñés however, and, already well in his 20s, spent several seasons with the Catalans' B-team, playing three years in the second division.
After the departure of legendary Andoni Zubizarreta and prior to the arrival of Vítor Baía, Angoy profited from some injuries to first-choice Carles Busquets to appear in nine La Liga matches. As the 1995–96 campaign drew to a close, both him and manager Johan Cruyff (whose daughter was married to the player) left the club; after an unassuming spell at Córdoba CF, he retired from football.
Angoy spent seven years (1996–2003) at NFL Europe side Barcelona Dragons's kicker, then switched to Italy with the Bergamo Lions (IFL). In 1999, he had an unsuccessful trial with the Denver Broncos, the reigning champions of the National Football League.
Three years later, Angoy was selected to NFL Europe's All-Offensive team.
- Qué fue de... Jesús Angoy (What happened to... Jesús Angoy); La Liga, 27 February 2014 (in Spanish)
- Angoy se atreve con la liga más espectacular del mundo (Angoy takes a shot at world's most spectacular league); El Mundo, 23 July 1999 (in Spanish)
- Un trampolín para el nieto de Cruyff (A trampoline for Cruyff's grandson); Marca, 18 November 2013 (in Spanish)
- Claymores make ideal start; BBC Sport, 14 April 2002
- Jesús Angoy. El español que rechazó jugar en los Denver Broncos. (Jesús Angoy. The Spaniard who refused to play for the Denver Broncos.); Diario AS, 18 March 2014 (in Spanish)
- 2002 All-NFL Europe League Team[permanent dead link]; at Hworth
- Jesús Angoy at BDFutbol