will a r9 280x bottlenck a phenom ll x4 960 @ 3.8ghz

Solution
A 280x should be able to run every modern game at at least high resolution.
The question is "Is the phenom 960 strong enough"

http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-5.html

The phenom ll x4 965 which is just above your processor lies in line with the first generation i7.
These are still decent gaming processors. Paired with an amd 280x you should be fine for gaming.
But if possible even upgrading to an i3 would be cpu upgrade. You would need a new motherboard and probably ram for this.
For example if I run skyrim at 720p on my 12 core i7 at 4 gigahertz and a geforce 780 ti, the game will probably max out close to 200 fps and not go any higher because of a bottleneck with the graphics card. This isnt bad because 200 fps is more than enough fps. "I dont really run at 720p" lol
 
A 280x should be able to run every modern game at at least high resolution.
The question is "Is the phenom 960 strong enough"

http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-5.html

The phenom ll x4 965 which is just above your processor lies in line with the first generation i7.
These are still decent gaming processors. Paired with an amd 280x you should be fine for gaming.
But if possible even upgrading to an i3 would be cpu upgrade. You would need a new motherboard and probably ram for this.
 
Solution
It will bottleneck but not much.

It will be a good system, its not like you are going to get horrible FPS. You may have ~10-15% less performance than the card offers at stock speeds. At 4GHz the 965 and 960 can handle a 760 without a bottleneck, so you will be fairly close to removing the bottleneck. In CPU intensive games it will be more apparent, but again, it wont be bad.

(Source, Owning a 965@4.22 and a 760)