Best CPU that will complement AMD Radeon HD 6950 for gaming only ?

6950 is right at the border between i3 and i5, but this was for 2nd gen sandy bridges.
I haven't seen any benchmarks addressing whether the new i3-3225 would possibly limit a 6950 or not. I would think with 5-15% performance bump it should pull just enough. Plus if you do hit a bottleneck it will be minimal and in limited number of games, so to a point you can consider it insignificant.

I'm not sure on the price right now, but do some checking between i3-2120, i5-2300/2400 and the i3-3225. See which one would work for your budget.

all those fit into 1155 socket, so one motherboard will be compatible with all.

i wouldsay the i5 2400 is probably the best idea if your on a tight budget... but preferabley a 2500k with a decent cooler for overclocking would be the ideal. currently a quad core is a better idea for gaming as games are getting more demanding and will only increase system demands as time goes on...
to my mind the days of dual cores regardless of threading and architecture are coming to an end (some would disagree but this is my opinion)... as games like max payne, bf3 show 4 cores as a requirement is quickly becoming the norm...
the dual core antizig mentioned is still a worthy cpu that should allow you to get the full potential from the card but some games just require more and sooner rather than later you would find that out...

Go for a 2500k and OC it