Jepsen retired the side in order, striking out one, to register his second hold of the season in Sunday's 7-4 win over the Mariners.
Jepsen struck out three and retired all four men faced in Friday's game against Seattle.
Jepsen signed a minor league deal with the Rangers on Thursday that includes an invitation to spring training.
Jepsen has agreed to a deal with Washington on Thursday, Jon Heyman of FanRag Sports reports.
Jepsen was released by the Diamondbacks on Saturday, MLB.com's Steve Gilbert reports.
Jepsen signed a minor-league contract with the Diamondbacks on Monday, MLB.com's Steve Gilbert reports.
Jepsen's option was declined by the Rays, making him a free agent, Marc Topkin of the Tampa Bay Times reports.
Jepsen was credited with his fifth hold of the season in Tuesday's victory over the Blue Jays, giving up only one hit during a scoreless eighth inning.
Jepsen notched his fourth hold with a scoreless inning against the Blue Jays on Friday in which he recorded a strikeout.
Jepsen has allowed eight hits and three runs over 9.1 innings since joining the Rays on July 14.