Jenkins, a 24-year-old who made his major league debut with 14 appearances for the Braves last season, was put on the Rangers' 40-man roster.
Feigl, who turns 26 later this month, spent all of 2016 on the disabled list at Triple-A Gwinnett while recovering from Tommy John surgery in April 2015. The Rangers assigned him to their Double-A Frisco roster.
Jackson pitched for the Rangers in each of the past two seasons. The 25-year-old righty has given up 17 earned runs over 18 innings in 15 career appearances in the majors.