Hailing from a humble background, Alcaraz worked throughout his teenage years as a builder's assistant in his hometown of San Roque González de Santa Cruz in the Paraguarí Department.

[3] Whilst Alcaraz was working as a builder at the age of 18, he met scout and football agent Carlos Bruni who took him to Argentina's Racing Club de Avellaneda.

On 14 May 2010, Alcaraz signed with Wigan Athletic on a free transfer for an undisclosed fee,[8][9] as his contract with Brugge was due to expire at the end of June;[10] his new manager, Roberto Martínez, stated that the player was in "the best form of his career" at that point.

[13] 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.

[16] 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.

[23] 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.

[25] 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.

[33] 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,[34] and went on to play all the matches (save one due to suspension) and minutes for the quarter-finalists.