Boscan, a ninth-year pro, had a 2.87 ERA in six starts for the Triple-A Indians, the most recent on Sunday.
"So he's got 100 pitches in the tank if we need to use him," manager Clint Hurdle said.
The Bucs needed the extra arm after having seven relievers throw 161 pitches in the 11-10, 12-inning loss on Friday.
Realistically, Boscan is not likely to see the Wrigley Field mound unless either Gerrit Cole on Saturday or A.J. Burnett on Sunday gets an early hook and long relief innings are needed.
The Cubs, who likewise went through seven relievers who made 134 pitches Friday, called for righty Brian Schlitter from Triple-A Iowa. Optioned to Iowa to clear room for him was Matt Szczur, who had hit the 12th-inning pop fly that dropped in front of a falling Gregory Polanco to give the Cubs their walk-off win.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer and on his podcast. This story was not subject to the approval of Major League Baseball or its clubs.