crochet rug

You could try a border. Try to loosen your stitches though, as tight stitches often result in more curl. A larger hook would help with this.
I do a lot of tunisian crochet which is notorious for curling. Adding a border to it takes out the curl.

I assume you're a seasoned crocheter and know about blocking
www.anniescatalog.com/knit/content.html?content_id=706&type_id=S&scat_id=4
(I don't know if that depends on whether the yarn is man-made)
Have you thought about putting on a fringe? Or bobbles? Or small curtain weights? Velcro if it's a rug?