Smith, 19, spent last season on loan in the Dutch second tier with FC Twente.
The Wales international is yet to make a senior appearance for City.
The Rs have also signed Tottenham midfielder Luke Amos on a season-long loan.
Amos made his first-team debut for Spurs at Newcastle last August, but an anterior cruciate ligament injury in September ended his season prematurely.
The 22-year-old had a loan spell with Stevenage during 2018, scoring two goals in 16 appearances.
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