He is the sixth Texas player with three hits in his MLB debut and the first since Nomar Mazara in 2016.
Smith, who played Monday's game at third base, was called up from Triple-A Round Rock after versatile infielder/outfielder Brad Miller was placed on the 10-day injured list with a right hip impingement.
Miller was removed from Sunday's game at Oakland with tightness in his hip in the fifth inning. He hit his seventh homer earlier in the game, and is batting .228 with 23 RBIs in 41 games.
Texas also recalled outfielder Zach Reks from Round Rock. He had two strikeouts in four plate appearances. Hard-throwing right-hander reliever Albert Abreu was designated for assignment.
Texas acquired Smith from the Yankees in the six-player trade last July that sent slugger Joey Gallo to New York. Smith was a second-round pick by the Yankees out of LSU in the 2019 amateur draft, and went into this season rated as one of the top 10 prospects for the Rangers.
Smith hit .273 with four homers, eight doubles, two triples and 29 RBIs in 40 games at Round Rock. He has started 17 games at third base, 14 at shortstop and nine at center field.
Reks hit .286 with three RBIs in six games in an earlier stint with the Rangers this season. In his nine games for Round Rock before his recall, Reks hit .417 with five homers and 11 RBIs.
The Associated Press contributed to this story.