The Rangers also activated right-hander Tony Barnette from 10-day disabled list ahead of Sunday's game in Chicago against the White Sox.
Grilli is expected to join the Rangers on Monday for a home game against the Boston Red Sox. The club will make a corresponding 25-man roster move at that time.
The Rangers need bullpen help as they lead the major leagues with 16 blown saves this season.
The 40-year-old Grilli was 2-4 with a 7.97 ERA over 26 2/3 innings with one save in 26 games with Toronto this season before being designated for assignment on June 27.
Grilli is 34-46 with 79 saves and a 4.18 ERA in 575 career appearances with the Miami Marlins (2000-01), Chicago White Sox (2004), Detroit Tigers (2005-08), Colorado Rockies (2008-09), Texas Rangers (2009), Pittsburgh Pirates (2011-14), Los Angeles Angels (2014), Atlanta Braves (2015-16) and Blue Jays (2016-17). He was a National League All-Star in 2013 when he posted 33 saves for Pittsburgh. He also saved 24 games for Atlanta in 2015.
Grilli was acquired by Texas from the Colorado in June 2009 and was 2-2 with a 4.78 ERA in 30 games as a setup reliever for the Rangers the rest of that season.
Pinto was hitting .311 with four homers and 18 RBIs in 46 games for High-A Down East this season.
Barnette was placed on the 10-day DL on June 16, retroactive to June 15, with a right ring finger sprain. He worked three scoreless innings in two outings on injury rehab assignment at Round Rock. Barnette is 1-1 with a 7.23 ERA in 23 relief appearances with the Rangers in 2017.
In addition, the Rangers optioned right-hander Tanner Scheppers to Triple-A Round Rock and designated right-hander Preston Claiborne, who is on option at Round Rock, for assignment to make room for Grilli on the 40-man roster.
Scheppers was purchased from Round Rock on June 19 and was 0-1 with a 6.75 ERA in five games with the Rangers.
Claiborne has spent most of 2017 with Round Rock, going 2-0 with a 1.37 ERA and 13 saves.