After falling out of favour at Manchester United, Rojo returned to Estudiantes on loan in January 2020, before making a permanent transfer to Boca Juniors in February 2021.

The defender spent most matches as a left-back and developed a reputation as a capable attacker, scoring his first goal in a 2–1 defeat against LDU Quito in the 2010 Recopa Sudamericana.

[10] Rojo made his Primeira Liga debut for Sporting on 19 August 2012, playing the entire match and receiving a yellow card in a 0–0 draw with Vitória de Guimarães.

[17] Sporting president Bruno de Carvalho later alleged that third-party owners of Rojo who were not representatives of Manchester United had pressured his club into selling the player.

[22] Rojo missed three matches for United due to difficulties in gaining a work permit, because of pending criminal charges in Argentina, where he is alleged to have had an altercation with a neighbour in 2010.

[24] Ten days later he made his debut at Old Trafford as United won for the first time in the season, playing the entirety of the 4–0 victory over Queens Park Rangers.

[28] During Manchester United's 2015 pre-season tour of North America, Rojo was expected to join up with the rest of the squad following an extended break granted after competing for Argentina in the Copa América.

However, passport issues reportedly caused Rojo to miss pre-season tour entirely, and the matter was said to have "angered" manager Louis van Gaal.

[29] In the 2016 FA Cup Final, which United won 2–1 after extra time against Crystal Palace, Rojo was booked in the first half for fouling Pape Souaré and was substituted for Matteo Darmian after 66 minutes.

[43] He made his FIFA World Cup debut in their 2–1 victory over Bosnia and Herzegovina at the Maracanã, playing the full match in defence, and contributing to Sead Kolašinac's own goal.

[47] At the end of Argentina's goalless quarter-final against Colombia in Viña del Mar, Rojo missed in the penalty shootout but his team advanced nonetheless.

[51] In the final on 26 June at MetLife Stadium, he was sent off in the first half for a foul on Arturo Vidal, as both teams ended the goalless game on 10 men and Chile again won on penalties.

[53] On 26 June, he scored the winning goal, once again against Nigeria, which his Argentina won 2–1 and secured the team's qualification for the knockout stage as group runners-up behind Croatia.

[54] In the round of 16 match against France on 30 June, he was booked after conceding a penalty in the 10th minute for a foul on Kylian Mbappé, which was later converted by Antoine Griezmann, who opened the scoring.

The injunction on his name was lifted in April 2015 due to concerns that other footballers could be suspected of the affair, but it remains in place to prevent the release of images of Rojo.