Elliott was signed as an undrafted free agent by the Dallas Cowboys after the 1992 NFL Draft, to compete as the replacement for kicker Ken Willis. He recovered from a pulled groin muscle in training camp, to be named the starter over Brad Daluiso.
Following the 1992 NFL Draft, Elliott was signed by the Dallas Cowboys to serve as Ken Willis's replacement as kicker. After recovering from a pulled groin muscle during training camp, he became the team's starting kicker, surpassing Brad Daluiso.