Azcona was introduced to motorsport at the age of six when his father bought him a kart, and he went on to contest Spanish karting championships throughout his childhood. In 2009 he finished second in the national Cadet class championship, and in 2010 placed fourth in the KF3 class.
In 2012, at the age of 15, Azcona stepped away from single-seater ambitions and moved into touring car competition, driving a Renault Clio in Class 2 of the CER alongside Diego Rodríguez. He secured his first professional victory the following year in the Spanish Renault Clio Cup and continued through the Seat León Eurocup, where he won four races in 2016 and finished runner-up behind Niels Langeveld.
In 2017, Azcona entered the Audi Sport TT Cup and won six races across the season — at the Norisring, Zandvoort, Nürburgring, and Hockenheimheim — finishing second in the overall standings behind Philip Ellis.
Azcona joined the TCR Europe series in 2018 driving a Cupra León for PCR Sport. His consistency across the season, with one win at Zandvoort and ten top-five finishes, was enough to edge Jean-Karl Vernay for his first major championship title.
For 2019 he stepped up to the World Touring Car Cup (WTCR) with PWR Racing, scoring his first WTCR victory at Vila Real and finishing sixth in the standings. However, the season ended in controversy at the final round in Malaysia: while attempting to pass championship contender Esteban Guerrieri for the race lead, Azcona made contact that pushed Guerrieri off the circuit from a title-clinching position. The collision ultimately denied Guerrieri the championship, and Azcona was penalised 30 seconds for the incident.
In 2021, Azcona ran a dual programme, contesting both the WTCR and the inaugural ETCR electric touring car series. Despite a slow start to his WTCR campaign, he captured a win at the penultimate round and finished seventh in the standings. In the TCR Europe championship, he dominated despite missing one round at Zandvoort, sealing the title in Barcelona before flying to the Czech Republic to compete in the WTCR races at Most the same day.
For 2022, Azcona joined Hyundai Motorsport as an official factory driver, with his primary objective being the WTCR title. The season was complicated by the mid-year withdrawal of the Lynk and Co team, disputes over Goodyear tyre failures, and the cancellation of several late-season rounds. Despite these disruptions, Azcona clinched the WTCR Drivers' Championship during qualifying for the FIA WTCR Race of Saudi Arabia, making him the last driver ever to win the title as the series was discontinued at the end of the season.
That same year he also contested the ETCR, won in the TCR class at the 24 Hours of Nürburgring, and finished fifth overall in ETCR with a single victory at Vallelunga.
Following the end of WTCR, Azcona remained with Hyundai in the TCR World Tour, continuing to represent the Korean manufacturer at the highest level of global touring car competition. He simultaneously expanded his programme with Porsche machinery, competing in the Porsche Supercup and Porsche Carrera Cup Germany with Hadeca Racing.
Azcona's career arc — from Spanish club racing at fifteen to back-to-back TCR Europe titles and a WTCR championship — marks him as one of the defining talents of the touring car generation that emerged through the TCR structure. His 2022 Hyundai campaign concluded the WTCR era and cemented his status as the championship's final champion.