Jennings threw three strong innings in Texas' 10-3 loss to the San Francisco Giants. He gave up one run and one hit, struck out four and walked none.
"Hopefully, I proved that I can throw the last four weeks," he said. "Hopefully that will prove to them that my arm's in pretty good shape."
Jennings had been projected to start the year in the minors after an awful 2008 season. The right-hander went 0-5 with an 8.56 ERA in six April starts, then spent the rest of the year on the disabled list.
The 30-year-old has had surgery on his flexor tendon twice in the past 19 months, first in August 2007 and again in January. He has a 1.98 ERA this spring.
"I can't throw any better than I've done," Jennings said. "At least I'm at peace with myself that I couldn't do any more. Whatever happens happens."
Rangers manager Ron Washington said decisions on the bullpen, as well as the final spot on the rotation and the last outfield spot, could come Wednesday.
"When it's not clear cut it's not clear cut," he said. "We might have something tomorrow. We might not. I hate standing here sounding like this but there's no decision made."
Barry Zito went seven innings for the Giants, yielding three runs and six hits. He struck out two and walked none.
"I wanted to be aggressive, throw strikes and let them get themselves out," said Zito, who has allowed nine walks in 31 2-3 innings this spring. "I'm excited to get it going right now."
Josh Hamilton hit a three-run homer off Zito in the third inning.
Matt Harrison lasted just 1 2-3 innings for the Rangers. He gave up five runs, two earned, and four hits with three walks.
"I felt pretty good and then all of a sudden I couldn't find the strike zone," Harrison said. "I felt bad. The way I pitched I'm pretty embarrassed. But I've pitched long enough to know I'll figure it out."
Harrison threw two innings in a minor league game after departing. ... With Emmanuel Burriss securing the starting job at second base, the Giants optioned INF Kevin Frandsen to Triple-A Fresno and reassigned INF Jesus Guzman to their minor league camp. ... Texas optioned INF Travis Metcalf to Triple-A Oklahoma City and outrighted LHP Kason Gabbard to its top farm team after he cleared waivers. ... Rangers LHP Dustin Nippert, slowed by a sore back muscle, threw batting practice and will be re-evaluated on Wednesday. ... Rangers 1B Chris Davis was sidelined for the second straight day with discomfort in his left patella tendon. Hank Blalock took Davis' place at first.