Acuña developed with the youth squads of Tigres UANL.[1] In 2008, he made his debut with the reserves in the Primera División A, making eight appearances that season.[2] He later made his Mexican Primera División debut for UANL on 19 October 2008 as a substitute in a 4–1 win over Monterrey, and scored his first professional goal in the 90th minute of the same match.[3] He also made two appearances for UANL in the 2009 InterLiga.[2]
In the 2009–10 season, Acuña made ten league appearances, scoring two goals.[2] The following year, he played his first full season of professional football, making 27 league appearances and scoring four goals.[2] He also appeared in the second leg of UANL's Clausura Liguilla series against Guadalajara.[4]
In the 2011–12 season, Acuña saw a sharp reduction in playing time, making only seven league appearances and two in the Copa Libertadores, as well as one appearance in the Apertura Liguilla against Pachuca.[2] In the first half of the 2012–13 season, he made two league appearances and two appearances in CONCACAF Champions League before being loaned out until the end of the season.[2]
Loan to San Luis
On 6 December 2012, Acuña was loaned to San Luis until the end of the season.[5] He made ten league appearances and three in the Copa Mexico for San Luis that year.[2]