PEORIA, Ariz. -- The Padres have made more than their share of splashy signings this offseason. But at the Peoria Sports Complex this spring, they're just as pleased with the depth acquisitions they've made over the past few months.

They made another on Wednesday.

The Padres and veteran infielder Rougned Odor have agreed to a Minor League deal with an invite to Major League Spring Training. Odor, a nine-year big leaguer who spent the bulk of that time with Texas, passed his physical Wednesday morning. He’s expected to start at second base on Thursday, manager Bob Melvin said.

“I know a lot about him -- I managed against him for quite a while,” Melvin said. “We’re looking at getting him an opportunity. We’re a little short on some infielders, especially with the [World Baseball Classic]. He’ll get an opportunity to play. … We’ll see what he has to offer.”

Odor, 29, will compete for a job as a lefty bat on what otherwise appears to be a righty-heavy Padres bench. He batted .207/.275/.357 in 135 games for the Orioles last season.

Then again, those struggles came in a bit of a different role for Odor, who served as the Orioles' regular second baseman last season. In San Diego, he'd presumably be asked to start only sporadically, while serving as a pinch-hitter against right-handers. Odor owns a .725 career OPS against righties.

The race for Padres bench spots is an interesting one. Fernando Tatis Jr. is ineligible to return from suspension until April 20, opening up an extra roster spot for the first 20 games. As things stand, there are two places available -- though it's unclear whether outfielder Adam Engel will be fully recovered from his strained right calf in time to crack the Opening Day roster. Engel is currently taking live at-bats and throwing, but is unable to run the bases.

If Engel were to begin the season on the injured list, that would free up another spot. Currently in the mix for those final 2-3 bench places: David Dahl, José Azocar and Brandon Dixon.

Add Odor to that list.

Bogaerts off to WBC
Xander Bogaerts struck out in the first inning of the Padres' 5-1, rain-shortened win over the Rangers, walked in the second inning, then promptly exited for a pinch-runner. He had a flight to catch.

Following Wednesday’s game against Texas, Bogaerts left to join the Netherlands at the World Baseball Classic. The Dutch team will compete in Pool A in Taichung, Taiwan.

Bogaerts, who arrived in San Diego after signing an 11-year megadeal in November, says he’s acclimating well to the Padres’ clubhouse. He doesn’t think his absence will be much of an issue -- and he hopes it’s an extended one.

“You never know,” Bogaerts said. “I could get back here after the first round. I could get back here after [the finals] in Miami. … Just got to go enjoy it and try to win.”

Martinez starts strong
Nick Martinez was slated to throw three innings in his second Cactus League start on Wednesday. But he was so efficient over those first three scoreless innings that he threw a fourth -- a bit more laborious, but also scoreless.

“Felt good,” Martinez said. “... I was like, ‘Hey, we got another inning here,’ so I was like, ‘Let’s get creative.'”

Martinez needed just 49 pitches to get through those four innings, as he sets himself up nicely to pitch for Team USA later this month. Martinez is tentatively slated to start against Mexico on March 12.

In the meantime, Martinez was thrilled to welcome Odor, his former teammate. They aren’t the only former Rangers in the Padres’ clubhouse.

“We’re the San Diego Rangers,” Martinez quipped.

And moments later, Nelson Cruz launched a solo home run, his first of the spring.