Wurz, who resides in Monte Carlo and competes under the Austrian flag, began karting across Europe in 2017, competing in the Rotax Max Challenge, WSK events, and FIA-sanctioned karting series. He was scouted into the Ferrari Driver Academy during his karting years.
Wurz made his single-seater debut in 2021 at the Vallelunga round of the Italian F4 Championship with Prema, winning the rookie class in Race 3. He also raced at his home round at the Red Bull Ring, and later that year won at the F4 UAE Trophy held in support of the Abu Dhabi Grand Prix.
For 2022 Wurz ran a full F4 UAE campaign with Prema, taking two wins and eight podiums across the season to clinch the title with a race to spare. He then contested the full Italian F4 Championship with Prema, finishing fourth in the standings after a strong run that included a maiden Italian F4 victory from pole at Monza. He also took a pair of podiums in ADAC F4 at Spa-Francorchamps and Zandvoort, finishing seventh in that series despite missing the second half of the season.
At the start of 2023, Wurz competed in the Formula Regional Oceania Championship in New Zealand for M2 Competition. He led from the opening round and won races at Teretonga, Hampton Downs, and Taupo to clinch the championship when title rival Callum Hedge suffered mechanical trouble.
Wurz then joined ART Grand Prix for the Formula Regional European Championship but endured a difficult campaign, missing the Spa round through illness and appearing in only a handful of further rounds before switching mid-season to Euroformula Open with CryptoTower Racing Team. He took a podium on his Euroformula Open debut at the Red Bull Ring and won a dramatic second race at Monza, concluding his campaign with a double rostrum at Barcelona to finish sixth in the standings.
In 2024, Wurz joined Jenzer Motorsport for the FIA Formula 3 Championship alongside Max Esterson and Matias Zagazeta. Points came on only one occasion — fifth place in the Melbourne feature race after starting 14th, benefiting from strong tyre management. He finished 22nd in the standings. He also participated in the final running of the FIA Formula 3 World Cup at Macau with Jenzer in 2023, qualifying 18th and finishing the qualification race 11th before retiring from the main event.
For 2025, Wurz remained in FIA Formula 3 but moved to Trident, partnering reigning FRECA champion Rafael Camara and rookie champion Noah Stromsted.
Wurz subsequently left Europe to join the revived Team Goh in Japan's Super Formula Championship. He has also competed in various sportscar categories, winning a race in the Porsche Sprint Challenge Europe at the Hungaroring in 2021 and later competing in the 2023-24 Porsche Carrera Cup Middle East at Bahrain International Circuit.
Wurz's father is Alexander Wurz, a two-time Le Mans 24 Hours winner and former Benetton, McLaren, and Williams Formula 1 driver. Charlie is the older brother of Oscar Wurz and competes under the Austrian flag despite residing in Monaco.
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