World of Warcraft is not that much of an intensive game that your CPU should be struggling to keep up with it.
It's already a core i3 and you shouldn't be noticing any bottlenecks with a 6670.
Are you sure that lag is not related to your system doing multiple things at the same time?
If not, you can safely upgrade to a r9 270 and perform at max settings on World of Warcraft on the same CPU.
If you are however playing other games that are CPU intensive and they lag as well, then you might need an upgrade.