Horton first represented Australia at the 2012 Junior Pan Pacific Swimming Championships in Honolulu, where he won gold in the 1500 metre freestyle in a championship record time of 15:10.07. At the same meet, he finished second in the 400-metre freestyle and 4th in the 800-metre freestyle. Two months later at the final leg of the 2012 World Cup in Singapore, Horton won the 1500 metre freestyle event in 14:54.25. At the 2013 Australian Youth Olympic Festival, Horton won gold in the 1500 metre freestyle event. Eight months later at the 2013 World Junior Championships in Dubai, Horton won five gold medals and a silver. He took out the 200 m, 400 m, 800 m and 1500 m freestyle events and alongside Luke Percy, Regan Leong and Blake Jones won the 4 × 100 m freestyle relay all in new Championships record times. The team of Horton, Leong, Isaac Jones and Jack McLoughlin finished second behind the British in the 4 × 200 m freestyle relay event. Horton qualified for his first senior team at the 2014 Australian Swimming Championships where he won the 1500 metre freestyle in 14:51.55 and finished second behind David McKeon in the 400-metre freestyle in 3:44.60, setting two new junior world records. Horton also finished 5th in the 200-metre freestyle in 1:47.36 which also set a new junior world record. At the 2014 Commonwealth Games in Glasgow, Horton won the silver medal in the 1500 metre freestyle in new junior world record time of 14:48.76 and narrowly missed the podium in the 400-metre freestyle finishing in fourth place in 3:44.91. In the 4 × 200-metre freestyle relay event, Horton alongside Thomas Fraser-Holmes, David McKeon and Ned McKendry finished as the fastest qualifies with Horton swimming the anchor leg in 1:49.17. In the final, Horton was replaced by Cameron McEvoy and they went on to win the gold in a new games record time of 7:07.38. Three weeks later at the 2014 Pan Pacific Swimming Championships in Gold Coast, Australia, Horton won the silver medal in the 800-metre freestyle in 7.47.73, the bronze medal in the 1500 metre freestyle in 14:52.78 and with McKeon, McEvoy and Fraser-Holmes won bronze in the 4 × 200-metre freestyle relay in 7:08.55. In April 2014, Horton became an ambassador for Horton's Heroes Water Polo team with the swimwear brand Speedo and in August 2014, after his breakthrough performances he was named the winner of the Georgina Hope Foundation Rising Star of the Australian Swim Team. At the 2016 Summer Olympics, Horton represented Australia in the 400 m freestyle, in which he won gold, and the 4 × 200 metre freestyle relay, in which he finished 4th with his teammates. He finished 5th in the final of the 1500 m freestyle. At the 2019 World Aquatics Championships, Horton won silver in the 400 m freestyle event where he came runner up to Sun Yang. In a controversial "stand-off" Horton refused to shake the hand of Sun or to stand on the winners' podium. Horton had previously called Sun a "drug cheat". On 28 February 2020, Sun was issued an 8 year ban by the Court of Arbitration for Sport for tampering with the doping control process, with calls to reissue medals from affected events, though the CAS clarified that Sun would not be stripped of any of his medals because "doping tests performed on shortly before and after the aborted doping control in September 2018 were negative" and "in the absence of any evidence that may have engaged in doping activity... the results achieved by in the period prior to the CAS award being issued should not be disqualified." Horton has been criticized for remaining silent on Australian swimmers who have faced punishments for violating anti-doping rules.
