Forget about a new cpu from that socket. Upgrade overall. But I would assume the bottleneck is GPU not CPU. The i7 870 is still reputable but lagging. Can you upgrade to newer platform? If not then I'd stress GPU upgrade first.
Your upgrade path is: keep GPU, and sell off the CPU/mobo/RAM and get yourself happy. That i7 is decent but 6 years old and will hold back your GPU. I'd sell now and look at the new Ryzen 5 as upgrade path.