How do I change my apple id country without a credit card?
It looks like your question is 2 fold:


  
  Can I accept an iTunes gift card from another country?
  Can I change my apple id country without providing a credit card?
  


Looks like in both cases it's a No.

1. Can I accept an iTunes gift card from another country?

From the Apple Forums


  You can't redeem it outside of the USA. You also can't change the
  iTunes Store country while any of its balance remains.


2. Can I change my apple id country without providing a credit card?

For this you can enter a credit card, but it's not charged unless you purchase an item from iTunes or the App Store. 

There appear to be a bunch of different hacks around this, but nothing definite from my estimation.