3:36 PM PT -- Darius Rucker's attorney, Mark Puryear, tells TMZ … "Darius Rucker is fully cooperating with authorities related to misdemeanor charges."

Darius Rucker got busted on a minor drug offense in Tennessee -- and from the sound of the charge he was booked on ... it basically amounts to an alleged handoff.

The country singer -- obviously famous from Hootie & the Blowfish -- was taken into custody Thursday in Williamson County, which is where he lives. He posed for this mug shot for the Sheriff's Dept. there ... and was booked on three separate charges, all misdemeanors.

Darius was arrested for two counts of simple possession/casual exchange of a controlled substance and one count of a violation of the state's vehicle registration law.

In terms of what DMV law cops think Darius broke ... they're saying he let his/tags expire on his car.

DR was brought into the jail around 10 AM PT, and he was released about an hour or so later -- we've confirmed Darius bonded out and is no longer in custody.

Unclear what exactly happened that led up to his arrest -- we're trying to get a hold of police now for further clarification.

We've reached out to Darius' team for comment as well ... so far, no word back.