Smith recently returned from a loan stint at Tranmere Rovers, making seven appearances for Keith Hill's League Two side in the three months spent at Prenton Park.
The forward previously spent a curtailed 2019-20 campaign on loan at Cambridge United, scoring eight times in 28(+6) appearances in the fourth tier last season.
The Academy graduate, who has also spent time on loan with Oxford United and Shrewsbury Town, has registered a total of 6(+5) appearances for the Royals first team, scoring his first league goal in a 3-2 defeat at Carrow Road back in March 2018.
Michael Duff's men are flying high in fourth place in League Two and Smith could make his Robins debut away at Forest Green Rovers this weekend. His Jonny-Rocks Stadium bow could come against Barrow on Tuesday night.
Everyone at Reading Football Club would like to wish Sam the very best of luck during his time with Cheltenham Town.