The agreement gives Jennings another chance to rebound from elbow problems that have plagued him since he returned to his home state after six seasons with the Colorado Rockies.
Jennings started just six games for the Rangers last year before season-ending surgery in May to repair a torn flexor tendon in his right elbow. Similar surgery ended his 2007 season with the Houston Astros in August.
The Dallas native was a combined 2-14 with a 6.91 ERA with Texas and Houston. He won 58 games for the Rockies from 2001-06, including a career-best 16 in 2002.
He is guaranteed just $15,000, but if added to the 40-man roster Jennings would receive an $800,000, one-year contract. He would be able to earn an additional $1.45 million in performance bonuses based on innings: $100.000 each for 110, 120 and 130; $200,000 each for 140 and 150; and $150,000 each for 160, 170, 180, 190 and 200.