Rodriguez was ticketed on May 31 for driving under the influence, speeding and improper lane usage. He was also charged in March with disorderly intoxication and resisting an officer in Miami. Those charges were eventually dropped.
The 24-year-old Rodriguez, drafted out of Temple, played in 12 games for the Bears in 2012, starting five. He had four catches for 21 yards.
Bears general manager Phil Emery said he was "extremely disappointed" in Rodriguez during OTAs last week.
"We have talked. Disappointed. I would use the word extremely. And we'll leave it at that," he said.
Information from ESPNChicago.com's Jeff Dickerson, ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.