Ok, well if its an individual asking for your credit card..NO..its not. Is it secure to use it on xbox live to pay for a live membership, YES, but it will automatically renew your membership. The best way to get a new membership or points, is to buy the cards from 7/11 or somewhere like that, ebay even.
It is not secure to give your credit card to the account in Xbox, since you didn't buy it. It is also not necessary to use the credit card for the payment and you can opt to pay using PayPal or a pre-paid subscription cards. Visit http://www.wikihow.com/Make-a-Payment-for-Xbox-Live for more details.