Tony grew up in Biloxi, MS and went to Notre Dame High School. After high school, Tony joined the military and served from 1966-1970. While in the military, Tony was a 19x skeet shooting champion. After his time in the military, he attended Ole Miss and was a member of the ROTC Rifle Team.

Throughout his college years, Rosetti was a 6x State Champion, 6x World NSSA Champion, U.S. International Champion, National Intercollegiate Skeet Champion, and a member of the U.S. Olympic Team. After college Rosetti continued to compete, earning 10 Champion titles (individual and team) from the National Skeet Shooting Association. He retired from shooting registered targets in 1992.

In addition to being inducted into the Mississippi Sports Hall of Fame, Tony has also been inducted into the Biloxi, MS Sports Hall of Fame, Mississippi Skeet Shooting Association Hall of Fame, and the National Skeet Shooting Association Hall of Fame.