Is there a monthly fee for using World of Warcraft Cataclysm

Yes; it is the same cost as for any version of World of Warcraft. You will need to buy the original game and all 3 of the other expansion packs before you can use Cataclysm though.

The monthly price is 14.95, but you can get a dollar or two price break if you buy 6 or 12 months at a time.