The Giants selected Morgan's contract from Triple-A Sacramento ahead of Monday's game against the Astros, Alex Pavlovic of NBC Sports Bay Area reports.
Morgan is hitting .241 with one home run, 14 RBI and 13 runs over 28 games this season at Triple-A Sacramento and will get a chance to see his first major-league action after being promoted. He's in line to serve as the backup catcher Monday after Daniel Susac was diagnosed with a fractured left patella.