Braylon Edwards -- Done In By Long Islands ... Cops Say

Braylon Edwards took down a handful of Long Island Iced Teas before he was popped for DUI in Arizona ... this according to the police report obtained by TMZ Sports.

We broke the story ... the former NFL star was arrested in Scottsdale around 2:40 AM on May 4th. Cops say Edwards was initially pulled over because his headlights were off.

During the stop, cops say Braylon reeked of booze ... so they asked him to perform a breath test -- but he REFUSED ... even after they told him a refusal would result in his driver's license being suspended for 1 year.

Eventually, he changed his tune -- and according to the police report, Braylon blew a .21 -- more than twice the legal limit.

Later that night, cops say he admitted having 3 Long Island Iced Teas at Oasis nightclub earlier in the evening ... but left because "I thought I was fine."

Edwards was ultimately charged with extreme DUI. For his part, cops say Braylon was very polite and cooperative throughout the process.