To make room on the 40-man roster, the team transferred Ryan Tepera to the 60-day injured list.
Kingham was designated for assignment by the Pirates on June 8, ending a 10-year run with the organization. The 27-year-old is out of options so he would have to be placed on waivers if the Blue Jays were to send him to the minors.
The Houston native has a 9.87 ERA in 34.2 innings with the Pirates this year. Last season, Kingham made his major-league debut, starting 15 games with a 5.21 ERA and 32 strikeouts compared to 17 walks.
The Blue Jays seem likely use Kingham out the bullpen given injuries to relievers including Tepera, Elvis Luciano and Ken Giles. They could also use him as a spot starter since he has started four games this season with Pittsburgh.