Politico said it was the first time Giffords, a former Democratic congresswoman from Arizona, has fired a gun since Jared Lee Loughner shot her in the head and killed six others in Tucson, Ariz., on Jan. 8, 2011.
On the seven-day tour, Giffords and her husband, former astronaut Mark Kelly, will meet with a coalition of people that support commonsense gun measures, such as gun owners, Republicans and hunters, Giffords' spokeswoman Pia Carusone told ABC News Monday.
Giffords and Kelly, who say they are proud gun owners, are on their way to Anchorage, Alaska.
The couple will also stop in North Dakota, North Carolina, Ohio, Maine and New Hampshire as part of the "Rights and Responsibilities Tour."
In April, the U.S. Senate defeated legislation that called for tighter background checks on gun purchasers.
Giffords and Kelly may meet with the senators who voted against the gun control proposal, Carusone said.