It must be knit in stockinette? Stockinette always curls. It's just the nature of the beast especially if you knit tight.
I'm sorry to say that even a border won't always make it behave well. It's worth a try though. You may need to make it several inches as a little one or two inch border probably will curl or fold in on itself. And make sure it's a non curling border like garter or seed stitch.