Broun sent a campaign email to supporters Friday, asking, "How would you like to start off 2014 with a brand new AR-15 for free?" WXIA-TV, Atlanta, reported.
Broun said in the email he one of the "most conservative members of Congress," and is constantly under attack for his beliefs.
"Democrats and liberal media would love to take away our guns and mandate every aspect of our lives," he said.
Supporters were invited to sign up for a drawing to win the semi-automatic rifle, which is valued at $1,300.
To enter the drawing, supporters need to provide their name, email address and zip code prior before Feb. 27 at Broun's campaign website.