Nicknamed "El Toro" (The Bull) due to his strength and dominating presence, he operated mainly as a central midfielder. He spent several years as a professional in Spain at Zaragoza and Deportivo, appearing rarely for the latter club.
Acuña was born in Avellaneda, Buenos Aires, Argentina, emigrating to Paraguay (his father's origin country)[2] at a young age and starting playing for Club Nacional in 1989. After five years, he decided to acquire the country's citizenship to play for the national team, eventually becoming the second most capped player in Paraguay's history, second only to Carlos Gamarra.
Consequently, Acuña attracted attention from Deportivo de La Coruña, which bought the player for five years and €11 million even though he was still due a five-match suspension from the previous season, where Zaragoza was relegated.[6] With the Galicians, however, he never appeared more than seven times in the league during his spell, also struggling with injuries[7] and being often loaned.[8]
Acuña first retired in 2007, finishing his career in Paraguay with Olimpia Asunción. However, in 2009, he came out of inactivity, signing with lowly Club Rubio Ñu; in 2012, the 40-year-old joined Club 12 de Octubre.
Like central defender Gamarra, Acuña appeared in three FIFA World Cup – 1998, 2002 and 2006 – and collected 100 caps in total, scoring five goals.[13][14] He played all the matches for the national team in all three editions, and was the first Paraguayan to be sent off in a World Cup when he elbowedGermany's Michael Ballack in the last minute of the 0–1 round-of-16 loss on 15 June 2002 (for a second bookable offense).[15]
In the build-up to the 2006 World Cup, Acuña made headlines in Sweden after reportedly having asked a FIFA employee to phone and try to arrange a date with a female photographer.[16] He retired from international competition on 11 June 2011 at the age of 39, captaining Paraguay in a friendly with Romania.[17]