Travis, 53, was previously arrested in February for public intoxication.
Grayson County Sheriff's Office said they responded on Tuesday to a report of a man seen lying near a road near Tioga, Texas, where Travis lives.
Travis had threatened to kill arresting officers and refused sobriety tests, Texas officials said.
Tom Vinger, a spokesman for the Texas Department of Public Safety, said a blood sample was taken from the country singer instead.
The 53-year-old, who began his career in the mid-1980s, has won seven Grammys and several Country Music Association awards.
Tuesday's incident, a car registered to Travis drove off the road, striking several barricades in a construction zone.
Sergeant Rickey Wheeler of Grayson County said Travis would also face charges of retaliation or obstruction.
"Travis had a strong odour of alcoholic beverage on his breath and several signs of intoxication," a statement from the sheriff's office said, adding he made "threats to shoot and kill the troopers working the case" while being transported.
On Wednesday, Travis made $21,500 (Â£13,700) bond, leaving jail wearing a clinical overall and no shoes.
A representative for the singer told the Associated Press there would be no immediate comment.