Praise be to Allaah.
It is not permissible to subscribe to credit cards unless one is forced to do so, because this is a riba-based contract, and riba is haraam according to the Qur’aan, Sunnah and scholarly consensus.
With regard to paying zakaah via credit card, if you have money saved to cover what you are going to pay, so that you will not have to pay any interest – as you mention in the question – then there is nothing wrong with paying zakaah by this method.
But if you do not have money saved to cover what you are going to pay, then this is considered to be a loan with interest from the bank, which is riba and is haraam, so it is not permissible for you to pay zakaah or anything else by this method. Allaah is Good and does not accept anything but that which is good.
And Allaah knows best.