Angeliño was born in Coristanco, Galicia. He joined Deportivo de La Coruña's youth setup in 2007 at the age of ten, after starting it out at Luis Calvo Sanz de Carballo. He spent six years at Dépor's youth system, being linked to FC Barcelona and Real Madrid due to his performances.
On 8 July 2012 Angeliño signed a four-year deal with Manchester City, being effective in January of the following year. Initially assigned to the under-18s, he also appeared regularly with the reserves. On 2 December 2014, Angeliño was an unused substitute in City's 4–1 away win against Sunderland. On 30 January 2016, Angeliño made his debut for the first team in a 4–0 away win against Aston Villa, coming on in the 81st minute to replace Gaël Clichy in the FA Cup.
Angeliño signed for New York City FCon loan in 2015. Angeliño made his professional debut for the club on 12 July 2015 in a 4–4 draw against Toronto FC. Angeliño came on for Kwame Watson-Siriboe in the 46th minute and played the entire second half of the match. He had his first interview for the club on 16 July 2015. He made his first start in a 1–0 defeat to New England Revolution, playing the full 90 minutes.
2016–17
Angeliño made his first appearance of the 2016–17 season and his Champions League debut on 24 August, as a substitute in a 1–0 win over Steaua București. His next appearance came on 21 September, starting in a 2–1 win over Swansea City in the EFL Cup. It was announced on 27 December 2016 that Angeliño would be loaned to Girona FC from 1 January 2017 to the end of the season. On 31 January it was announced that, having not made a single appearance for Girona, Angeliño would instead be loaned to RCD Mallorca. He made his debut on 5 February, in a substitute appearance in a 2–1 loss to Real Oviedo.
Manchester City re-signed Angeliño on 3 July 2019 after triggering a buy-back clause in his contract. Angeliño made his debut in the 2019–20 Premier League season on 21 September, coming on as a half-time substitute for Benjamin Mendy in a 8–0 routing of Watford at the Etihad.
On 31 January 2020, having made 12 appearances for Manchester City, Angeliño was loaned to German Bundesliga club RB Leipzig until the end of the season.
