The Rangers also called up switch-hitting infielder Luis Sardinas for a second time. But Odor will get most of the starts at second base until Jurickson Profar is ready to come off the DL.
"I'll move Sardinas around and give Odor four to five games a week at second base," manager Ron Washington said.
Odor is a left-handed hitter, and he went right into the lineup on Thursday with left-hander Franklin Morales on the mound for the Rockies.
"I'm going to let him face [left-handers and right-handers] and then make a decision," Washington said. "If there is an issue, one will get right-handers and one will get left-handers. Right now, I'm going to let him face them all."
Wilson was the Rangers' Opening Day second baseman after Profar began the season on the DL with a torn muscle in his right shoulder. Wilson got off to a strong start, but he had just two hits in his last 27 at-bats, to go along with 10 strikeouts, dropping his average to .224. Murphy is hitting .211, but he went on the DL after straining his neck during Wednesday's 9-2 loss to the Rockies.
The Rangers were also looking for a spark to an offense that had scored five runs in three games against the Rockies and was hitting .233 in the last nine games. Second base was the one position Texas felt it had an alternative, and that's why the club brought up the two young prospects.
"It was a chance to improve our offense at second base," general manager Jon Daniels said. "We've been scuffling at a few spots, and second base we felt internally we had a chance to upgrade. These are guys who play with energy, run hard and do the little things. So did Josh and Donnie, both those guys gave it their all."
Odor, 20, will be making his Major League debut on Thursday night. He was hitting .279 with six home runs and 17 RBIs in 32 games, including .421 in his last nine games at Frisco. Odor was the Rangers' Minor League Player of the Year in 2013, when he hit .305 with 85 runs scored, 41 doubles, six triples, 11 home runs, 78 RBIs and 32 stolen bases at Class A Myrtle Beach and Frisco last year.
"I feel very happy to be here and fulfill my dream," Odor said. "I'm ready to play baseball. If I'm here and they called, that means they need me. So I'll be ready to play."
Odor was with the Rangers in Spring Training and received consideration when Profar went down with an injury. But he had played in only 30 games at Double-A last season, and Texas decided to go with Murphy and Wilson instead.
"We wanted him to get off to a good start offensively and make sure he wasn't a Spring Training mirage," Daniels said. "The reports were very positive. He is swinging the bat very well, his defense is good, his energy is good. We felt bringing both would take the pressure off each, so they don't feel they have to carry the load."
Sardinas, who turns 21 on May 16, will be in his second stint with the Rangers this season. The switch-hitting infielder was also with the club from April 19-26, going 1-for-3 with a run scored over three games. Since returning to Frisco on April 28, Sardinas has batted .294 with three doubles, a triple and four RBIs in eight games.
"I just expect them to both play baseball," Washington said. "If they weren't performing, they wouldn't be here. They're playing good baseball and we believe in them. There will be issues, but we'll work them through it. We'll bridge that gap and get them to play the way we want them to play."
Sardinas, in his role as utility infielder, will have to play third base if Adrian Beltre needs a day off. Sardinas has never played third base in the Minor Leagues, but the Rangers feel he can handle it.
"He can catch the ball over there," Washington said. "A couple days over there and he'll have it down. The kid is sharp."
Profar could be back by the beginning of June. He is taking batting practice and has begun a throwing program. Profar is expected to report to Surprise, Ariz., next week to start take living BP and possibly be used at designated hitter in extended spring games.