Drafted 76th overall out of high school by the Buffalo Sabres in the 1988 NHL Entry Draft, Carney starred at the University of Maine for three years during which time he made various All-Star teams for his fine play. He joined the Sabres in 1991 after spending much of the year with the U.S. National team, but he played only parts of three seasons with the organization before being traded to Chicago.
With the Hawks, Carney matured and developed into a solid defenceman and during his four full seasons there he helped anchor a developing corps of talent. But the team never advanced very far, and late in the 1997-98 season he was traded to the Phoenix Coyotes. Just weeks earlier he had represented the USA at the 1998 Winter Olympics in Nagano, Japan.
After four seasons in Phoenix, Carney was dealt to the Anaheim Mighty Ducks in 2001-02 and was a valuable asset on the Ducks blueline, helping the club reach the Stanley Cup final in 2003 against the eventual Cup champions from New Jersey.
Carney went on to play parts of four seasons with the Ducks before being acquired by the Vancouver Canucks at the 2006 NHL trading deadline. Carney's stint with the Cancuks was short lived as the free agent defenceman was signed by the Minnesota Wild in the summer of 2006.