Hornsey was the Ray Guy Award winner last season at Memphis and averaged 43.1 yards per punt for his career. He had 75 punts of 50 yards or more and 13 of more than 60 yards, including a career-long 79-yarder.
Hornsey took part in the New York Jets' rookie minicamp in the spring. He grew up in Australia and played Aussie Rules Football. The Cowboys can only hope he is half as good as their other Aussie-born punter, Mat McBriar, who punted for the club from 2004-2011.
Chris Jones is the incumbent punter and has had a solid camp so far.