Barinaga joined Patronato from Colón in 2016.[4] After four years progressing through their youth ranks, Barinaga made the breakthrough into Gustavo Álvarez's first-team squad in 2020.[3] He initially featured during pre-season, notably scoring in a friendly match with Atlético Paraná on 11 January.[5][6] Barinaga made his senior debut on 14 December 2020 during a 4–0 defeat in the Copa de la Liga Profesional away to Rosario Central, as the midfielder replaced Fernando Luna with thirteen minutes left.[3][7][8]