Iñaki Peña signed for Alicante CF when he was just five years old. In 2009, Villarreal CF was interested in the precocious player, where he began to stand out, especially in 2011, when he was chosen as the best goalkeeper of the Arona tournament. Barça had its eye on him and a year later he came to the Masia.

In his first season between the posts of the Barça Under-14 team, he won the league and was one of the keys to the team. His skill and play allowed him to grow as a player until he reached Barça B in the 2018/19 season. The keeper alternated between the B squad and the first team in the season 2020/21 and was part of the squad that lifted the Copa del Rey. 

In the winter of the 2021/22 season the keeper left for Galatasaray on loan before returning in the summer of 2022 to the club. In January 2023 he was officially registered as a first team player. 

That same season, 2022/23, Peña made his first debut in the Champions League against Viktoria Plzen before making his first appearance in La Liga for the blaugranes away at Valladolid in May 2023.