Alcaraz was loaned to ACF Fiorentina in 2002, but the Italians soon faced bankruptcy and regrouped in the Lega Pro Seconda Divisione. He then had a trial at U.S. Città di Palermo, but nothing came of it.

In January 2003, Alcaraz signed for Portuguese club S.C. Beira-Mar. After seven appearances in half a season, he became a defensive mainstay at the Aveiro side. In 2005–06 he helped them return to the Primeira Liga, playing 31 matches.

Alcaraz joined Club Brugge KV in Belgium on 30 April 2007, with the deal being effective as of July.

In November 2008, Alcaraz received his first call-up to the Paraguayan national team at the age of 26. He was picked for the squad present at the 2010 FIFA World Cup; on 14 June, in the group stage opener against Italy, in just his seventh cap, he headed home through a powerful header following a set piece in an eventual 1–1 draw in Cape Town, and went on to play all the matches (save one due to suspension) and minutes for the quarter-finalists.

On 14 May 2010, Alcaraz signed with Wigan Athletic on a free transfer for an undisclosed fee, as his contract with Brugge was due to expire at the end of June; his new manager, Roberto Martínez, stated that the player was in “the best form of his career” at that point. He scored his first goal for the club against Sunderland on 11 September 2010, netting in the 86th minute for a 1–1 home draw.

Alcaraz caused widespread controversy on 6 November 2011, when replays showed him spitting at Wolverhampton Wanderers defender Richard Stearman during a 3–1 defeat at Molineux Stadium. He was handed a three-game suspension due to his actions, but later issued an apology.

On 7 May 2012, Alcaraz scored the game’s only goal at Blackburn Rovers to retain the Latics’ top-division safety, whilst relegating their opponent to the Football League Championship. He won the 2013 FA Cup, featuring the full 90 minutes in the 1–0 upset of Manchester City. However, only three days later, with him on the pitch again, Wigan were relegated from the top division following a 1–4 away loss to Arsenal.

On 9 July 2013, after becoming a free agent, Alcaraz moved to Everton on a two-year deal as both he and goalkeeper Joel Robles followed coach Martínez to the club. He made his competitive debut on 29 December after an injury struck his start to the season, featuring the full 90 minutes in a 2–1 home win over Southampton.

On 26 April 2014, Alcaraz scored an own goal in the first minute of a 0–2 loss to Southampton. On 1 January of the following year, he received his first sending off as an Everton player, being shown two yellow cards in a 0–2 away defeat against Hull City which was the team’s fourth successive of the festive period.

On 2 August 2015, aged nearly 33, Alcaraz signed a one-year contract with newly promoted La Liga side UD Las Palmas with the option of a second one. He scored his first goal on 23 September, helping best Sevilla FC 2–0 at home.

During his spell at the Estadio Gran Canaria, Alcaraz made only seven competitive appearances due to injury. On 29 January 2016, he left by mutual consent.

In February 2016, Alcaraz agreed to a deal at Club Libertad. He made his Paraguayan Primera División debut the following month at the age of 33, in a 2–1 home victory against Cerro Porteño.

On 2 January 2019, Alcaraz signed with Club Olimpia of the same league. In his debut campaign, he was part of the squad that won the national championship.