Cappelletti started his early career as a full-back, but transformed into centre-back with Südtirol.
Born in Cantù, Lombardy, Cappelletti started his career at Como and then Cantù San Paolo. In January 2009 he was signed by Sicily club Palermo. He was a regular member of Primavera under-20 team in 2009–10 season.
In August 2010 he left for Serie B club Padova along with Davide Succi, with option to buy half of the registration rights for €400,000 and €500,000 respectively. Cappelletti made his debut on 2 October, replacing José Ángel Crespo at half time. That season he played 3 games in the Italian second division, substituted Crespo twice and left-back Trevor Trevisan once. He made his only start in 2010–11 Coppa Italia. That match Padova used a 3–4–3 formation and he was one of the 3 defenders.
On 1 July 2011, he left for another second division club Sassuolo along with Karim Laribi. However, he did not play any match for the first match but played for Sassuolo’s Primavera (literally “Spring”) team as overage player. On 5 January 2012, he moved to fellow second division club Juve Stabia.
On 4 July 2019, he signed a 2-year contract with Vicenza.