Shia LaBeouf Kisses Mystery Woman After Mia Goth Split

Shia LaBeouf is back in the dating game ... and he's playing it out in public nearly a year after his split from Mia Goth.

TMZ has obtained video and photos of the actor getting handsy with a mystery woman during a flirty Saturday night out in New Orleans just days after his recent arrest.

Shia was at a bar just off Bourbon Street, where he spent more than 45 minutes locked in with a brunette who clearly had his full attention. The two stood hand in hand under the club lights on an upstairs balcony overlooking the bar.

At one point, she rested her hand on his chest while smiling up at him and Shia leaned down to whisper in her ear before sealing it with a kiss.

The pair shared multiple kisses, held hands tightly and stayed glued to each other throughout the night. In the footage, Shia appears relaxed and affectionate, pulling her close, murmuring in her ear and going back in for more.

Witnesses tell us he was drinking and seemed a little tipsy, but in great spirits.

The PDA packed night comes on the heels of a rough stretch for the actor. As we reported ... Mia, who split from Shia nearly a year ago, wants him to seek rehab and manage his drinking.

We also broke the story … LaBeouf was arrested in New Orleans last week and charged with two counts of simple battery following an altercation with a group of men.