Smolinski has had multiple hits in all three of his starts with the Rangers and is the first Ranger ever to record eight hits through his first four big league games. George Wright had seven in 1982.
Smolinksi left Friday's game with a left elbow contusion after getting hit by a pitch in the second inning. X-rays were negative.
Smolinski, who stays away from social media in an effort to keep his head down, said his agent broke the news to him Thursday night.
"I'm not really going to get caught up in the numbers," Smolinski said. "I feel like my mentality's good. I feel like I'm ready to compete at every bat ... and to hit every pitch."
West retired all six of the batters he faced Thursday night in his debut, becoming just the second Ranger in history to have a debut where he retired all of at least six batters faced. The first was Neftali Feliz in 2009.
"I'm trying to come in, get outs and throw strikes," West said. "Honestly it's kind of everything and more than you think it could be. You're trying to control your emotions when you get out there, but it's definitely a different feeling."
T.R. Sullivan is a reporter for MLB.com Read his blog, Postcards from Elysian Fields and follow him on Twitter @Sullivan_Ranger. Grace Raynor is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.