Rodríguez had spells with River Plate and Vélez Sarsfield in his youth career prior to joining Banfield.[3] His professional career got started in 2015 with Banfield of the Argentine Primera División. He made his debut on 1 November, coming on as a second-half substitute in a league defeat to Rosario Central.[1][4] In July 2017, Rodríguez joined Italian football by signing for Serie A side Genoa.[1] After making his Genoa debut in the Coppa Italia on 30 November 2017 versus Crotone, Rodríguez left the club on loan in January 2018 to join Vitória Setúbal of the Primeira Liga.[5] He didn't make a senior appearance in six months with the club.[1]
On 9 August 2018, Chilean Primera División's Unión La Calera completed the loan signing of Rodríguez.[6][7] He scored his first senior goal against Deportes Antofagasta on 18 August.[1] Overall, Rodríguez netted three goals in twenty games for them.[1] He returned to his parent team on 30 June.[8][9] Rodríguez had interest from other Chilean teams upon returning to Genoa, though the ANFP prevented the right midfielder from joining another top-flight outfit as it went against league rules regarding multiple contracts in a single campaign; his father and agent Leonardo appealed the ruling.[9] He terminated his Genoa contract in August.[10][11]
In August 2019, Rodríguez rejoined Unión La Calera on a free transfer.[10][11] In 2023, Rodríguez played for Unión Española,[12] and switched to Audax Italiano the following year.[13]
