Yes and no...
Without actually getting a true credit card, you can purchase one of the "Visa Gift Cards" available at the checkout lanes of most grocery stores, walmarts, etc. Even any bank. You can get them for anywhere from $10 to $100 or more. There is generally a $2 to $4 fee on top of the actual "dollar value" of the card, with banks usually having lower fees than grocery stores/walmarts.
Google checkout will accept these cards just fine.