''I understand the significance of my actions,'' he said in a statement released by the Cardinals on Friday, ''and right now I am taking the necessary steps to handle my personal business.''
DeKalb County court records say Abraham was taken into custody June 29 and released the same day.
The 36-year-old Abraham, a five-time Pro Bowl player, has been absent since the Cardinals opened training camp a week ago.
''I am very thankful for the support from my family, friends and especially the Cardinals organization during this time in my life,'' he said. ''I am looking forward to being back with my teammates in the near future.''
Police said he was at the wheel of a 2013 Dodge Challenger that had stopped in the center southbound lane of a suburban Atlanta road the afternoon of June 29, Brookhaven, Georgia, police said in an incident report that Abraham smelled of alcohol and failed voluntary sobriety tests - including reciting a portion of the alphabet. Police said Abraham remained asleep for several minutes after police arrived, despite an officer shouting and pounding on his doors and windows
It was his third alcohol-related arrest.
In 2012, he was arrested on an obstruction charge in Atlanta after he repeatedly refused to leave an area taped off by firefighters and police. A police report said he appeared intoxicated, smelled of alcohol, was unsteady on his feet and slurred his speech.
And in 2003, Abraham pleaded guilty to driving while impaired in New York after he drove his SUV into a fire hydrant and light pole. Police had said his blood alcohol content measured more than three times the legal limit.
Abraham had 11 1/2 sacks as outside linebacker for the Cardinals last season, earning a fifth Pro Bowl appearance. He is the active leader in career sacks with 133 1/2.
He is entering his 15th NFL season, having played six years with the New York Jets and seven with the Atlanta Falcons before signing a two-year contract with the Cardinals a year ago.
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