Calabresi spent his entire youth career at the Roma youth academy. In 2015, he was officially signed to a professional contract by the club.
That same year, Roma loaned him to Serie B’s AS Livorno Calcio. He made a total of 10 appearances for the club.
In 2016, Calabresi was loaned to Serie B’s Brescia Calcio. He became a regular starter for the club, appearing in a total of 44 games.
The following year, Calabresi was loaned to yet another Serie B club. This time it was Spezia Calcio. He only played 2 games for the club.
In 2018, Rome loaned Calabresi to Serie B’s Calcio Foggia. He appeared in 9 games for the team.
In June 2018, Serie A’s Bologna signed Calabresi for an undisclosed fee. Calabresi made a total of 18 appearances for the club.
In 2019, Bologna loaned him to Amiens SC of the French Ligue 1.
Arturo Calabresi represented Italy at all youth football levels from U17 to U21. In total, he made 52 appearances for the national squads.
He took part in the 2013 UEFA U17 Championship where Italy won silver.
He also represented his country at the 2013 FIFA U17 World Cup.