Scottsdale police told azcentral.com that Kirk and some of his friends were allegedly throwing rocks at cars on Feb. 3 as they were leaving the Waste Management Phoenix Open.
"The suspects were intoxicated and leaving the WMPO. As they were walking through a parking lot, security personnel observed them throwing rocks at cars and breaking a window of at least one of them," the police told the newspaper.
The Cardinals said they were aware of the incident before drafting the former Texas A&M wide receiver 47th overall.
"We knew about it," coach Steve Wilks said on Tuesday. "We did our own independent research on it and we felt very good about the information that we received and that's why we moved forward in really drafting him. As I stated before, we want to bring in great character guys and I think Christian is one of those guys.
"I think the situation is going to resolve itself here in a couple of months. And with it still being an on-going legal issue, I'm not going to go into it any further than that."
Before, throughout and after this year's draft, Cardinals coach Steve Wilks and general manager Steve Keim consistently discussed their desire to select high-character players -- including Kirk.
The 21-year-old receiver was a standout at Saguaro High in Scottsdale before playing at Texas A&M.
ESPN's Josh Weinfuss contributed to this report.