Cuadra was promoted into
Racing Club's senior squad in 2017, following eight years in the youth system. He made his professional debut on 12 March during a 3–0 win versus
Lanús. Three appearances later, Cuadra scored for the first time by netting the winning goal in a 2–3 win away to
Quilmes. In January 2019, Cuadra joined
Unión Santa Fe on loan. On 17 January 2020, he then joined
Gimnasia La Plata on loan until 30 June 2020. After playing for
Cobreloa in the
Primera B de Chile, on second half 2021 he returned to the Chilean football and joined
Unión La Calera, being loaned to
San Luis de Quillota. On 9 February 2022, Cuadra joined
Banfield on a deal until the end of the year. In the second half of 2024, Cuadra returned to Chile from
Greece and joined
Magallanes. The next year, he switched to
Santiago Wanderers. He joined
Deportes Temuco for the 2026 season. ==Career statistics==