Olivo was placed on the 15-day disabled list with a strained right groin after injuring himself in Monday's 3-2 loss to the Rays.
Carp flew from Tucson, Ariz., to Florida on Tuesday and rejoined the team in time for batting practice, but was not in the lineup against left-handed starter Matt Moore in Tuesday night's game.
Carp sprained his right shoulder on Opening Day in Tokyo and has spent the past three weeks with Tacoma, where he's struggled at the plate while regaining his timing, batting just .137 (7-for-51) with two doubles and four RBIs in 13 games. But he did have hits in three of his last four outings.
"It's relieving, very refreshing," Carp said after exchanging greetings with teammates. "I've been working real hard to get ready. It's been a grind and I'm happy to be here.
"I feel pretty good. The arm strength is still getting there. It's going to take some time. It was a pretty bad injury. I didn't think it was, but the doctors told me it would take some time. I've been turning corners every week and this last week I've been pretty normal. Hopefully this next week I get back to 100 percent."
Manager Eric Wedge said Carp would be worked back into playing time in left field, first base and designated hitter. With rookie Jesus Montero splitting time with John Jaso at catcher now that Olivo is out, some of that time figures to come at DH.
Olivo remained with the team in St. Petersburg. He'll have further tests done by team doctors when the club returns to Seattle on Friday.
Olivo strained his right groin muscle in the ninth inning while fielding a ball in front of the plate and turning quickly to throw to first base with his foot planted in the Tropicana Field turf. He had to be helped off the field and said the pain was worse than when he had a similar injury in the 2011 Spring Training that kept him out three weeks.