Upvote:5
According to the Bycyklen For Tourists page, you can set up an account online before you arrive. A credit card is required, but because it's online and therefore doesn't require a chip, it should work with your US card.
The hourly rate is DKK 30, which is currently about US$4.50. Whether you would consider this a "ripoff" or not is up to you. There are also packages available to reduce the price.