Yes they do make devices that can run credit cards over a telephone service.
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As mentioned above, they do sell devices that can run credit card information through a telephone line. Many businesses around here, if what you're trying to do involves a business, have small credit card machines or even ATM machines that basically plug straight into a phone line. Every transation made makes the credit card machine dial out to the credit card processor to record the transation, and it works the same as a PC dial-up modem.
There's really nothing to it, other than making sure it is behind a DSL filter should you use DSL.