AMERITRADE COMMERCIALS SAY "call 1-800-xxx-xxxx to set up a 'cash account' " So I don't think you can buy stock with a credit card, but it wouldn't hurt to try. Paying interest on the card would't be wise though. If you get miles, some rewards, or cash back fine.
I am not aware of a broker that will accept credit cards. You can deposit convenience checks into your account, but be aware these checks can be very expensive. CreditWorks offers a way around this by accepting credit cards for payment of memberships through PayPal. You do not truly participate in the market, but you do make 19.47% APR on the memberships. http://www.creditsense.com