The normal expression is "Random act of kindness". It means doing something nice for no particular reason. The phrase "on me" means that I will pay for the drink and the treat (something sweet to eat, perhaps).

Maybe it came from this picture. It looks like mis-read handwriting to me ... http://www.funnyjunk.com/funny_pictures/4141313/an+act+of+kindness/

Lanna; a "Random act of kindness" is when one is especially helpful to a stranger. "The treat's on me" is paying for, or buying something, often food or drink, for someone. For example, I invite some friends out for drinks at the pub. I tell them "Get whatever you want. The treat's on me," or "it's my treat," meaning "I'm paying for everything, it's my gift for you."