Born in Sant Carles de la Ràpita, Tarragona, Catalonia, Rangel represented CD Tortosa, CF Reus Deportiu, Girona FC, UE Sant Andreu and Terrassa FC in his homeland, never in higher than Segunda División B. In summer 2007, he signed for Swansea City in the English League One on a one-year performance-related deal, for an undisclosed fee – countryman Roberto Martínez was the team’s manager.

In his first season, Rangel played a massive role as the Swans returned to the Championship after a 24-year absence, as league champions. He scored his first goal for them on 27 November 2007, netting eight minutes from time in a 1–0 home win against Hartlepool United; only two weeks later, again at the Liberty Stadium, he netted in a 3–0 success over Southend United and, in April 2008, he was one of five team players to make the PFA League One Team of the Year alongside Ferrie Bodde, Garry Monk, Andy Robinson and the league’s top scorer Jason Scotland.

On 5 September 2008, Rangel signed a new contract until June 2010. He continued to feature prominently in the following years and, in mid-February 2010, agreed to an extension until June 2011.

In November 2011, Rangel was voted best defender in the Premier League. He played 34 matches during the season, helping the team retain their league status.

Rangel scored his first goal in the English top flight on 25 August 2012, in a 3–0 home win against West Ham United. On 8 March 2013, he signed a new contract with Swansea, keeping him at the club until 2016.

Rangel was believed to qualify to represent Wales on residency grounds, but was ruled ineligible in July 2012 as he had not had five years of continuous education in the country.

On 18 January 2013, Rangel drove around Swansea with his wife Nikki to distribute food to the homeless. He told CNN: “We went for something to eat in a local sandwich chain and overheard the manager saying they had to throw out food as they were about to close for the night. My wife, Nikki, who is a very caring and charitable person, asked if we could have them for the homeless rather than see them thrown in the bin. They agreed and we drove around Swansea for over an hour, but couldn’t find any homeless people as it was so cold out on the streets with all the snow. We decided to tweet a plea and we were guided to a local charity shelter who looked after the homeless.” He was so pleased with the reaction to his gesture he confirmed that he would be helping out again.

On 5 April 2013, Rangel announced plans to hold charity auctions with his wife and teammates Chico Flores, Ben Davies, Jonathan de Guzmán, Pablo Hernández, Michu and Itay Shechter, to raise money for the Severn Hospice in Telford, Maggie’s Cancer Centre in Swansea and The Christian Lewis Trust Kids Cancer Charity – among the top prizes on offer at one of the auctions were Rangel’s personal box for the game against Manchester City, and a visit to a Formula One garage during qualifying of the German Grand Prix. He was inspired to do this by Nikki, who has had three family members diagnosed with cancer.

On 19 April 2015, one month after again extending his link, now until 2017, Rangel was selected in The Football Manager Team of the Decade at the Football League Awards. On 14 November 2017, he was named as club captain after Leon Britton stepped down to become a player-assistant manager.

Rangel spent time in the 2018 off-season training with Indian Super League club Bengaluru FC during their tour of Valencia. On 15 August, he joined Championship side Queens Park Rangers on a one-year contract.