A nice idea, but pretty much impossible. It would cost hundreds of dollars for the gold alone, and to get it made would cost a fortune on top if that, and if you were to change your details at all you'd have to get it remade.
And also, it is impossible to make a business card out of solid gold. The gold in earrings isn't pure gold, it's a mix of metals to make it hard enough. It would be too soft to stay in shape properly, if it was pure gold.
An idea instead would be to have it made in platinum, and inlay the words in gold. Overall it would be cheaper and more practical.
Also, if you give away a solid gold business card to every client, your talking thousands of dollars.
Hope I helped :)