Popa started practising youth football with his hometown club Farul Constanța at age seven, and two years later moved to the nearby Gheorghe Hagi Academy.[1] He returned to his former side in 2018, going on to make his senior debut in a 1–0 Liga II win over Viitorul Târgu Jiu on 30 September.
Astra Giurgiu
Popa joined Liga I team Astra Giurgiu in the summer of 2019, but did not feature in any matches during his first year in the top flight. On 14 February 2020, he was loaned out to Liga II side Rapid București for the remainder of the season.[1]
On 11 July 2020, in a league derby against Petrolul Ploiești, Popa was given two yellow cards and sent off for stepping out of the goal-line twice during a penalty kick; Petrolul missed the subsequent third shot and the game finished goalless.[2]
On 14 November 2020, upon his return to Giurgiu, Popa registered his Liga I debut by starting in a 1–1 draw at Dinamo București.[3] On 22 May 2022, he played the full match as Astra lost 2–3 after extra time to Universitatea Craiova in the Cupa României final.[4] He appeared in 15 games all competitions comprised during the 2020–21 campaign, which ended in relegation for "the Black Devils".
Voluntari
On 11 August 2021, Popa was transferred to Voluntari for an undisclosed fee,[5] with Astra Giurgiu reportedly retaining 50% participation rights in a co-ownership deal.[6] On 19 May 2022, he was again runner-up in his second successive Cupa României final after a 1–2 loss to Sepsi OSK.[7]
Three days after the final, the Gazeta Sporturilor daily wrote that five-time defending champions CFR Cluj made a €300,000 offer to sign Popa,[6] but on 17 June 2022 the Voluntari Board of Directors decided that he would not be sold for less than €1 million.[8]
On 8 June 2023, Italian club Torino confirmed the signing of Popa for an undisclosed period.[9]
On 4 August 2024, after failing to record his official debut for Torino, Popa returned to his home country on a one-year loan at CFR Cluj.[10] He made his club and European debut on 22 August, in a 1–0 home win over Pafos in the UEFA Conference Leagueplay-off round.[11]
Popa's paternal grandfather, Gheorghe, was also a professional footballer.[14] He too played as a goalkeeper for Farul Constanța, between 1969 and 1977.