Albu started out his professional career at Concordia Chiajna in 2015, where he spent several seasons playing in the Liga I before relegating to the second division. Following loans to Academica Clinceni, UTA Arad, and Rapid București, respectively, he signed a permanent contract with the latter in 2021.
On 4 March 2017, Albu recorded his first league goal in a 1–1 draw against the same opponent.[6] He amassed totals of 99 appearances and three goals in the top flight for "the Green Eagles", before relegating to the Liga II at the end of the 2018–19 campaign.[7]
On 16 June 2021, Albu was loaned again to Rapid București,[9] totalling 36 games and a career-best seven goals in all competitions during the 2021–22 season.
Rapid București
In the summer of 2022, Albu joined Rapid București on a permanent basis after the team paid a previously-agreed €150,000 to Concordia Chiajna.[10] On 23 April 2023, he scored the only goal of a home derby victory over FCSB in the Liga I.[11]
On 25 February 2024, he and his teammate Andrei Borza were expelled from the squad for an undetermined period—later revealed as one match—because they partied in a nightclub after a 1–3 loss to Politehnica Iași.[12]
^ ab"Vedeta de pe maidan » Fotbalistul crescut în cartier a ajuns titular în derby-ul Rapid - FCSB" [The Star from the Streets » The football player who grew up in the neighborhood became a starter in the Rapid - FCSB derby]. Gazeta Sporturilor. 11 August 2021. Retrieved 5 February 2024. Albu was a central defender in the small, amateur leagues in which he played, then remainded a centre-back for Chiajna, with which he relegated from the first league to the second. [...] Poenaru told them he was going to convert Albu from a defender to a midfielder, which he did.