Replacing Santana, making his Major League debut, will be right-hander Sean O'Sullivan, who is 5-2 with a 6.02 ERA pitching in the hitter-friendly Pacific Coast League for Triple-A Salt Lake.
Kelvim Escobar's injection into the bullpen will have to wait another week. Escobar was placed on the 15-day disabled list with shoulder tenderness to make room for O'Sullivan.
An MRI was taken of Santana's elbow on Monday, but no results were available. Santana said he wasn't concerned, mainly because it isn't in the same area, inside the elbow, as the ailment that cost him the season's first five weeks.
After a superlative effort in Detroit on June 5, Santana couldn't sustain his momentum in Florida, absorbing some rough treatment by the Rays. Lasting 4 2/3 innings, he was cuffed around for eight hits and six earned runs, walking two and striking out three. He didn't have anything close to the command he'd shown in coming within one out of a complete game in Detroit, falling behind and grooving too many pitches in hitters' counts.
"I'll be OK," Santana said. "Nothing too bad."
Escobar, who went five innings in Detroit on June 6 in his first appearance since October 2007, hasn't pitched since that night. His shoulder, subjected to labrum surgery last July, will not hold up well enough for him to start, but he has been cleared for bullpen duty.
Escobar, Scioscia said, is expected to be activated next Monday when he's eligible to come off the disabled list.
Right-hander Shane Loux, who has begun to throw again after shoulder inflammation sent him to the DL, could emerge to add depth in the rotation if he makes good progress.
Scioscia doesn't have many starting options left with Matt Palmer, who made his first three Major League starts for the Giants last season, having inherited Escobar's spot.
Palmer is set to go on Wednesday against 2008 National League Cy Young Award winner Tim Lincecum in the series finale.
O'Sullivan has made 10 starts for Triple-A Salt Lake, having yielded 61 hits and 15 walks in 49 1/3 innings with 35 strikeouts.
"He's a sinker/slider guy with a pretty good change," said Angels catcher Jeff Mathis, familiar with O'Sullivan from Spring Training and Cactus League play. "He's like [Jered] Weaver -- not overpowering but good command, moving his fastball in and out."