charge port problem

Hey guys I'm using an Iphone 5 16GB and recently I've found that my charger doesn't work properly so i change the cable and the problem is still there.

My iphone won't charge BUT when I put a small piece of paper or something like that under the "cable jack" (sorry I don't know how to call it) and it works perfectly.

So my question is: is there any way to fix this problem ??? Or can I replace the charger port ???