Garton has pitched 44 games in relief over the past two seasons for the Rays, going 1-3 with a 5.26 ERA and one save in 44 games, and he is expected to be assigned to Triple-A Tacoma. He's pitched in seven games over three stints with Tampa Bay this year and is 0-1 with an 8.71 ERA.
Since Garton was on the 40-man roster, he would have had to clear waivers to be available. The Mariners also acquired All-Star first baseman Yonder Alonso from the A's for outfielder Boog Powell earlier Sunday.
Garton goes on to Seattle's 40-man roster, with catcher Tuffy Gosewisch designated for assignment to open a spot. Garton is 2-0 with a 1.64 ERA and four saves in 24 games, including one start, with Triple-A Durham this year.
"Garton has a little Major League experience and throws 92-94 with an above-average cutter," Dipoto said. "He has very good history at the Minor League level."
Marjama, 28, provides some catching depth at Triple-A Tacoma following Gosewisch's DFA. He has hit .274 with nine home runs and 51 RBIs in 72 games with Triple-A Durham, but has never been in the Majors and still has six years of club control.
"Marjama has been a good player at every level," Dipoto said. "He's an athletic catcher who can catch and throw and has a good history with the bat. We're looking forward to seeing what he can do when given a Major League opportunity. He was a Triple-A All-Star this year and a guy we feel pretty good about moving forward with."
Misiewicz, 22, is a left-handed pitcher who went 8-5 with a 4.75 ERA in 23 starts between Class A Advanced Modesto and Double-A Arkansas. He was an 18th-round Draft pick out of Michigan State in 2015.
Renigifo, 20, is an infielder who hit .250 with 11 home runs, 44 RBIs and 29 stolen bases in 102 games with Class A Clinton this season. He signed with Seattle as an international free agent in 2013.
Gosewisch played in 11 games with Seattle earlier this year and hit .071 (2-for-28). He batted .219 with four homers and 28 RBIs in 65 games with Tacoma.
Peterson claimed by White Sox
D.J. Peterson, the Mariners' first-round pick and the 12th overall selection in the 2013 Draft, was claimed off waivers by the White Sox on Sunday after being designated for assignment seven days earlier.