Arce played for Boca Juniors' youth team.[2]Deportivo Riestra of Primera D became Arce's first senior club in 2012.[3] He remained for one year, 2012–13, and scored eighteen goals in thirty-four matches as the club missed out on promotion in the final versus Ituzaingó.[3] In July 2013, Arce joined Primera B Metropolitana's Almagro.[1] He made his professional debut on 19 August during a home loss to Atlanta, prior to scoring his opening Almagro goal against Barracas Central on 14 October.[1] In total, Arce scored twelve times in eighty-eight games in three seasons with Almagro.[1] January 2016 saw Arce join Argentine Primera División side Quilmes.[1]
Four appearances followed before he left Quilmes.[1] Arce subsequently joined Patronato.[1][4] He scored on his second start, in a 4–2 victory over Arsenal de Sarandí.[1] Arce scored four further goals in eighteen matches for Patronato in 2016–17.[1][2] On 16 July 2017, Unión Santa Fe signed Arce.[1][5] However, he departed six months later following zero first-team appearances for the club; appearing as an unused substitute in the Primera División twice in September.[1][6]San Martín of Primera B Nacional became Arce's sixth senior career club in January 2018.[1][7] He sealed a return to Almagro on 30 June 2018; a team now in Primera B Nacional.[1]