Dallas needed a kicker after losing Dan Bailey to a groin injury Sunday at San Francisco.
Nugent spent training camp with the New York Giants but lost a training camp battle with Aldrick Rosas.
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The Bengals released Nugent last December after he struggled on both field goals and PAT kicks.
He passed the 1,000-point mark for his career last season, and his 132 points and 33 field goals in 2011 are team records.
He shares the team mark for longest regular-season field goal (55 yards).
Nugent was one of the best kickers in college football from 2002-04, helping the Buckeyes to a national championship as a sophomore and serving as team captain as a senior.
He won the Lou Groza Award in 2004.
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