Carter's blood-alcohol level tested at 0.14, said Texas Department of Public Safety trooper Johnny Hernandez. The state's legal limit is 0.08.
He was charged with misdemeanor possession of less than 2 ounces of marijuana after the drug was found in his car, Hernandez said. Carter was pulled over in the Mission area for failing to signal a turn, and had bloodshot eyes and slurred speech, police said.
The 31-year-old Carter was arraigned Friday and being held in the Hidalgo County jail.
In 2003, Carter guided the Cowboys to a 10-6 record and the playoffs in their first season under coach Bill Parcells. But he was released in training camp before the 2004 season.
He started briefly for the New York Jets before poor play and drug-related arrests ended his NFL career. He played in the Arena Football League before a brief tryout last year with the Miami Dolphins.