To make room for Kingham, left-handed pitcher Thomas Pannone has been optioned to triple-A Buffalo.
Kingham, 27, was acquired from the Pittsburgh Pirates in exchange for cash considerations earlier this week.
Through 14 appearances this season, Kingham has struggled mightily with a 9.87 ERA and 54 hits allowed in 34.2 innings pitched.
Pannone has appeared in 23 games and made two starts for the Blue Jays this season. He has a 5.91 ERA with 36 strikeouts.