Crivello started his career as a youth player with Mondello club Parmonval, before being scouted and signed by Juventus in 2009.
In 2013 he joined Lega Pro Prima Divisione club Frosinone, with whom he won two consecutive promotions and made his Serie A debut in 2015. He was also part of Frosinone's 2018 squad that won their second Serie A promotion in the club's history.
In 2018 he joined Serie B club Spezia. In August 2019 he rescinded his contract with Spezia and joined hometown club Palermo (Serie D level) as a free transfer.[2] He was part of Palermo's squad that won promotion to Serie C and then to Serie B in 2022.
On 6 January 2023, after appearing sparingly for the Rosanero in the first half of the club's 2022–23 Serie B campaign, Crivello was loaned out to Serie C club Padova until the end of the season.[3]
On 1 September 2023, Palermo announced to have agreed with Crivello to release him from his contract.[4]
On 31 January 2024, Crivello signed for Serie C club Monterosi on a contract until the end of the season.[5]
After suffering relegation with Monterosi and being released by the end of the season, Crivello signed for Eccellenza Sicily amateurs Athletic Club Palermo on 14 September 2024.[6]
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