Cook, 29, was charged with a misdemeanor after the deputy searched the car and found a plastic bag containing two grams of marijuana, Carlson said.
A voicemail message left for Texans spokesman Tony Wyllie was not immediately returned Thursday.
Cook, who lives in Missouri City, joined the Texans in 2006 and played in all of the team's games last season. He previously had played for the Tampa Bay Buccaneers, who drafted him in 2001.
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