Bozhin made his professional debut for Krylia Sovetov Samara on 3 June 2013 in the Premier League relegation play-off second leg against Spartak Nalchik, coming as a substitute on the 81st minute.

During the 2014–15 Russian Football National League season, Bozhin made 17 appearances and scored his first goal for Krylia Sovetov.

Bozhin, eventually, made his debut in the Russian Premier League on 8 August 2016 in a 0–1 away loss against FC Spartak Moscow, coming on as a substitute on the 81st minute.

In summer 2018, Bozhin signed for Fakel Voronezh, making 37 appearances and scoring 2 goals in the 2018–19 Russian Football National League.

He later moved to Torpedo Moscow the next summer as a free agent, making 25 appearances and scoring 4 goals in the following 2019–20 Russian Football National League season.