Rome fouled on his first two throws before recording a throw of 59.57 meters (195-5 feet) on his final attempt.
The 6-foot-4, 305-pound Rome, who will be 36 in December, finished 31st in the 41 competitors. The top 12 advanced to Tuesday's finals.
The top qualifier was 2008 gold medalist Gerd Kanter of Estonia with a throw of 66.39 meters (218 feet).
Germany's Robert Harting, the 2011 world champion, was second at 66.22.
Erik Cadee of the Netherlands took the 12th and final qualifying spot at 63.55 (208-6).
Six throwers met the Olympic A standard of 65 meters, which earned automatic qualification. The next-six best throws qualified for Tuesday's finals.
The top American finisher was Jason Young of Lubbock, Texas, with a throw of 62.18, which placed 18th.
The U.S.'s Lance Brooks of New Berlin, Ill., finished 21st with a best throw of 61.17 meters (200 feet 8 inches).
More Sports Headlines
Seahawks ink QB Wilson to 4-year, $87.6M extension M's deal Happ, Lowe at trade deadline Seahawks open camp with WRs as position of focus Late putback foils Storm in 67-66 loss 6:36 p.m. Local favorite Lehman leads 3M Championships 4:34 p.m. Woods in contention at Quicken Loans after a 5-under 66 4:34 p.m. Pettersen tames Turnberry, takes 2nd-round lead 4:34 p.m. Kyle Busch starts drive for 4th straight win from pole 4:21 p.m.
Our new comment system is not supported in IE 7. Please upgrade your browser here.