From 2011 to January 2013, Ciurria played for Castellarano's youth system, before moving on loan to Spezia, with whom he played in the Campionato Primavera 1 in the second part of the 2012–13 season. At the end of the season he was bought outright by Spezia,[2] making his first-team debut in the 2013–14 season; Ciurria made his Serie B debut for Spezia on 24 August 2013, in a 0–0 against Cittadella.[3] He made five appearances in the Serie B and three appearances in the Coppa Italia.[4]
Ciurria played two more seasons at Spezia, during the 2014–15 season (one league game and two cup games)[4] and in the 2015–16 season, in which he played more frequently, scoring a goal in 18 appearances in the Serie B, and making three appearances in the Coppa Italia.[4]
Loans to Südtirol and Siena
In summer 2016, Ciurria was loaned to Lega Pro club Südtirol.[5] He made 19 appearances in the 2016–17 season, and a game in the Coppa Italia Lega Pro.[4] In January 2017, Ciurria returned to Spezia, who then sent him on loan Siena;[6] he scored three goals in 15 appearances in the Lega Pro.[4]
Pordenone
In summer 2017, Ciurria was sold outright to Pordenone.[7] In the 2017–18 season, he scored six goals in 29 appearances in the Serie C.[4] Ciurria helped Pordenone with the league title in the 2018–19 season, marking the club's first promotion to the Serie B;[8] he scored three goals in 37 games.[4]
In the 2019–20 Serie B season, Ciurria scored five league goals in 35 appearances, and made one Coppa Italia appearance.[4] The 2020–21 season was a prolific one for Ciurria, seeing him score nine goals and make 11 assists in 36 league games – he was the league top assist provider.[9]
Monza
On 31 July 2021, Ciurria joined fellow Serie B side Monza on a three-year deal.[10] He made his debut on 14 August, in a 2–1 Coppa Italia defeat to Cittadella in the first round.[11] Ciurria helped Monza to their first Serie A promotion, after winning the promotion play-off final against Pisa.[12]
Ciurria made his Serie A debut for Monza on 13 August 2022, as a substitute in a 2–1 home defeat to Torino.[13] He first played as a starter on 18 September, assisting Christian Gytkjær in Monza's first-ever Serie A win, 1–0 at home against Italian giants Juventus.[14] Ciurria helped Monza to an 11th-place finish in the league.[15] On 10 August 2023, Monza renewed his contract until 30 June 2026.[15]