The right-hander will try to lead the Rays to a fifth consecutive win over the Baltimore Orioles in Monday night's opener to the AL East foes' first series this season.
Tampa Bay placed Matt Moore on the DL on Tuesday because of an ailing left elbow, then put Alex Cobb there before Sunday's series finale in Cincinnati. Cobb strained his left oblique while pitching seven innings in Saturday's 1-0 win over the Reds.
They join Jeremy Hellickson, who hasn't pitched this season while he recovers from elbow surgery.
The Rays (7-6) couldn't complete the series sweep after that effort, falling 12-4 on Sunday, and long reliever Cesar Ramos lasted only two-plus innings while taking Moore's spot in the rotation. Veteran left-hander Erik Bedard, who started the season in the minors, is expected to take Cobb's place.
Reliever Joel Peralta has also been dealing with an illness.
"Nobody's going to feel sorry for you and I don't want us to feel sorry for ourselves, either," manager Joe Maddon told the team's website.
Archer (1-0, 1.38 ERA) will try to help his short-handed club by adding to his promising start. After going six innings to beat Toronto in a 7-2 victory April 3, he tossed seven innings in Kansas City on Tuesday before the Rays scored in the ninth to win 1-0.
Archer went 1-0 with a 3.97 ERA in two starts last season against Baltimore, which dropped 11 of the final 13 games in last year's series. Tampa Bay also won five of its final six road games versus the Orioles.
Baltimore (5-7) was routed 11-3 by visiting Toronto on Sunday after winning four of six. The Orioles' 1-4 start was their worst since they opened 1-11 in 2010.
While his team has started the season in uneven fashion, Wei-Yin Chen has been consistently lackluster. The left-hander has given up four runs and failed to pitch past the sixth inning in each of his two starts.
Chen (1-1, 6.75) allowed a career-high 12 hits in a 4-3 loss to Boston on April 3, then gave up nine to the New York Yankees in a 14-5 victory Tuesday.
The Orioles have plated 10 runs in four subsequent games. They fell behind 11-1 on Sunday before Chris Davis hit his first homer of the season in the eighth and Matt Wieters followed with his third in six games.
"As an offense, we definitely want to score some more runs early in the game," said Davis, who led the majors with 53 homers last year. "When you go up there and put up a run early, you've got to continue to score runs."
Chen allowed two runs in each of his three starts versus the Rays last season and has a 2.13 ERA in his last six against them, going 2-1.
Ben Zobrist is 10 for 23 (.435) in his career against Chen. He had a pair of two-run homers Sunday.
J.J. Hardy, who returned from back spasms Saturday, is 1 for 7 with two strikeouts against Archer. Wieters and Adam Jones are each 0 for 6.