Alcaraz played for Deportes Infantiles de Villa Elisa,[3] before joining the youth academy of Racing Club in 2017.

[4][5] Alcaraz made his professional debut with Racing Club in a 1–1 Argentine Primera División tie with Atlético Tucumán on 26 January 2020.

[6] He scored the winning goal of the 2022 Argentine Cup Final against Boca Juniors in extra-time sparking a large melee, and being one of ten red cards.

[9] On 14 January, Alcaraz made his Premier League debut in a 2–1 away victory against Everton, replacing Roméo Lavia in the 61st minute.

[18] On 31 January 2025, Flamengo announced that they had reached an agreement for Alcaraz to join Premier League side Everton for the remainder of the 2024–25 season.