The 29-year-old has been optioned to triple-A.
MacIver was claimed off waivers by the Rangers on Nov. 5, 2025 but he spent the beginning of this season in triple-A.
His only time in the majors came last season with the Athletics, when he recorded three homers, nine RBIs and three stolen bases in 33 games.
In a corresponding move, the Blue Jays have also designated infielder Tyler Fitzgerald for assignment.
Kirk has been out of the lineup since the first week of April when he had surgery for a broken thumb. The timeline for his recovery was announced to be six weeks.
Tyler Heineman and rookie Brandon Valenzuela have been sharing catching duties with Kirk out.