A Georgia sorority girl's not letting her recent arrest get her down ... 'cause she was grinning from ear-to-ear in her mug shot -- and, her smile's got social media users in a tizzy.

Lily Stewart -- a 20-year-old university student from the University of Georgia -- was arrested earlier this month and booked on a speeding in excess of maximum limits charge, a misdemeanor in the state.

Unlike President Donald Trump's scowl in his mug shot, Lily decided to go with the Miss America look, like she just won the lottery -- instead of a one-way ticket to a holding cell.

TMZ has obtained the incident report ... where the officer claims he observed her driving 79 miles per hour in a 55 mph zone at around 10 in the morning. He says he pulled her over, cited her for the speeding ticket and actually let her go initially.

Unfortunately, the run-in with police apparently didn't do anything to quell Stewart's alleged need for speed ... 'cause this officer says mere minutes later he saw her driving 84 in a 55 -- and arrested her.

As you can imagine ... people online are in Lily's corner -- with some joking they've got no idea why she was arrested, but they're sure she's innocent of all charges.

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BTW ... Lily clearly thinks a good picture's a good picture, regardless of why it was taken -- 'cause she decided to post the mug shot along with her favorite comments from other social users.

We've reached out to Lily ... so far, no word back.