The Jan. 25 arrest came after a call of a suspicious person who was wandering the hallways checking door handles, said Irving police Officer David Tull.
After determining Glenn was "intoxicated or disoriented," officers arrested him on a public intoxication charge, Tull said. A subsequent search turned up a small amount of marijuana, leading to a misdemeanor charge of possessing less than 2 ounces of the drug.
Tull said Glenn was released on bond the morning after the arrest. Glenn also had outstanding traffic warrants in the Dallas-Fort Worth suburb of Roanoke.
A phone call to James Gould, Glenn's agent when he was released by the Cowboys in July, wasn't immediately returned.
Glenn had consecutive 1,000-yard seasons for the Cowboys in 2005-06 before two operations on his right knee knocked him out of the first 15 games in 2007.
Last summer, Glenn refused to sign a split contract that would have given him only $500,000 of his $1.74 million base salary if he had been unable to play because of the injured right knee. The Cowboys released him at the start of training camp, and he never signed with another team.
Glenn has 8,823 career receiving yards and 44 touchdowns in 12 seasons, including six in New England and one in Green Bay.