[8][9] He made his footballing debut with his local team Young Meteors Tamale[10] playing for them from 2004 to 2010, before being scouted by Dreams FC, an Accra based club at the age of 16.

[17][18][19][20] He made his debut on 16 September in a UEFA Champions League tie, playing the full 90 minutes in a 4–0 win at home to Maccabi Tel Aviv.

On 27 February, Rahman made an error which allowed Southampton's Shane Long to score in the 42nd minute; he was substituted for Kenedy at half time but Chelsea eventually won 2–1 at St.

[23] On 2 August 2016, FC Schalke 04, confirmed that Rahman had moved on a season-long loan to the club after failing to impress the new Chelsea manager Antonio Conte during pre-season.

[24][25] Rahman told the local newspaper Ruhr Nachrichten that Conte advised him to leave on loan because he preferred more defensive players than him.

[26] Rahman made his competitive debut for the Gelsenkirchen team on 20 August, as a winger instead of a defender in a 4–1 victory against FC 08 Villingen in the first round of the DFB-Pokal.

[27] He made his league debut on 27 August, coming on for Sead Kolašinac in the 62nd minute of an eventual 1–0 loss at Eintracht Frankfurt on the first day of the season.

[32] On 2 September 2019, the last day of transfer window, Rahman was again loaned out in a season-long deal, this time to newly promoted La Liga side Mallorca.

[43] Baba Rahman was selected for Ghana's final squad at the 2022 FIFA World Cup, and provided an assist during his side's opening match against Portugal; he produced the cross which was headed into goal by Osman Bukari.

In 2021, he donated football materials and equipment to his former school and to the Tamale Juvenile Unit to help upcoming sportsmen within the northern part of Ghana.