You will struggle to run any of the latest games with that CPU. I wouldn't recommend it.
If you are looking at an RX 480 then I assume you're hoping to game in 1080p with High or possibly Ultra settings in the majority of games and get about 60 fps?
To avoid nasty CPU bottlenecks and disappointment I'd recommend something like an i5 6500K.
The RX 480 may be cheap, but it needs a good CPU to get the most out of it.