The deputy who stopped him early Tuesday was responding to a family disturbance call, according to an affidavit. The caller had said there was a "disturbance between her and her husband," and that he had driven off and was possibly drinking.
When the deputy stopped the car driven by Jones, 46, and with the plate number given by the caller, he "detected a strong odor of alcohol," according to the affidavit.
Jones told the deputy he had consumed a bottle of Sake wine while having dinner with his wife at a sushi restaurant at about 8 p.m. Monday, the affidavit said. After getting into an argument with his wife, Jones said he walked home, about three miles away, the document said. When the argument continued at home, he left to go to another of his residences "to get away from his wife."
Jones was booked into Travis County Jail at 12:37 a.m. local time, and his bail was set at $3,000, according to Kristen Dark, senior public information officer at the Travis County Sheriff's Office.
CNN has reached out an attorney who has represented Jones in the past.
Jones claims he tested below the 0.08 legal limit and that a "countywide dragnet" was started because of a low number of DWI arrests in Travis County.
In a statement Wednesday, Jones said: "In Travis County, if they believe they smell alcohol, they take you in to the jail for testing. Once I was tested, I was found to be under the legal limit, so not guilty of a DWI under the Texas statute. I have talked to counsel, and they believe it will be a mere formality to have the case dismissed."
But a reading of 0.08 or above is not the only factor in arresting a motorist, according to the Texas Department of Transportation.
"In Texas, a person is legally intoxicated and may be arrested and charged with Driving While Intoxicated (DWI) with a .08 BAC (blood or breath alcohol concentration)," the department says. "However, a person is also intoxicated if impaired due to alcohol or other drugs regardless of BAC."
Jones tested at 0.076 and 0.079 and failed parts of the one-leg stand and walk and turn tests, according to the affidavit.
Speaking about the experience on his show, Jones said: "It was quite the experience to see what was going on in this country and to experience it myself," the InfoWars website reported.
Jones was released shortly after 4 a.m. Tuesday after bonding out on a personal recognizance bond, according to Dark.
The DWI charge is a class B misdemeanor, according to the court document.