McManus will likely handle the kicking duties while Matt Prater serves a four- game suspension for violating the NFL Policy and Program for Substances of Abuse.
Prater is eligible to return after the Broncos' Oct. 5 game against Arizona.
McManus was set to be released by the Giants on Tuesday. He connected on both of his field goal attempts and recorded touchbacks on 10-of-11 kickoffs during the preseason.
The Temple product spent the 2013 preseason with Indianapolis.
Denver also waived kicker Mitch Ewald, an undrafted rookie from Indiana, to open a roster spot for McManus.