Santiago caught the attention of a wider rugby audience during the 2015 World Cup with his pace and stepping skills, having scored memorable tries, two against Georgia (in which he was named "Man of the Match") and one against Tonga.

His clean breaks and distance covered were also noteworthy,[2] thus making significant contributions to Argentina's fourth place in the tournament.

[3] Cordero scored one try for the Argentinian side that beat the Barbarians 49–31 in the 2015 Killik Cup match, held at Twickenham on 21 November 2015.

He joined Exeter Chiefs in the Premiership Rugby in early 2018 as a medical joker, and became a full-time player for the 2018–19 season.

[9] On 6 January 2019, Cordero left Exeter to join French side Bordeaux in the Top 14 competition ahead of the 2019-20 season.