Tenaglia began his youth career with Argentino de Saladillo, prior to becoming a member of the Boca Juniors system and then having subsequent spells with Deportivo La Lola and Huracán de Saladillo.[3] In 2014, Tenaglia joined Atlanta.[3][4] Two years later, in October 2016, he made his senior career debut during a Primera B Metropolitana fixture with San Telmo.[2][5] He made nineteen league appearances in 2016–17 as Atlanta reached the promotion play-offs, before losing in round one to Deportivo Español; which was Tenaglia's final game for the club, he was sent off in the 89th minute.[2] On 23 August 2017, Talleres completed the signing of Tenaglia.[6][7]
Tenaglia made his debut for Talleres on 10 December 2017, in a 2–0 victory away to Colón in the Argentine Primera División.[2][8] He scored his first goal on 29 September 2019, netting his team's first in a 3–2 away loss against Independiente.
On 12 January 2022, Tenaglia was loaned to La Liga side Deportivo Alavés for 18 months.[9] On 20 August 2023, after helping the club in their return to the top tier, he signed a permanent four-year contract.[10]
^"Tenaglia será albiazul hasta 2027" [Tenaglia will be white-and-blue until 2027] (in Spanish). Deportivo Alavés. 20 August 2023. Retrieved 22 August 2023.