At the young age of five, Iñaki Peña signed with Alicante CF. In 2009, Villarreal CF took notice of his impressive talent, which continued to shine in 2011 when he was named the best goalkeeper of the Arona tournament. A year later, Barcelona recruited him and he joined La Masia.

Peña’s first season with the Barça Under-14 team was a success, as he played a key role in helping the team win the league title. His abilities as a goalkeeper allowed him to progress as a player, eventually leading to his promotion to Barça B for the 2018/19 season. He split his time between the B squad and the first team in the 2020/21 season, and was part of the team that won the Copa del Rey.

In the winter of the 2021/22 season, Peña went on loan to Galatasaray before returning to Barcelona in the summer of 2022. In January 2023, he was officially registered as a first team player.