They do. I've had payments taken from various credit cards for as little as 5cents.
The CC company will TAKE anything, it's the merchant who wants to avoid small amounts as the points they give back to the CC processor on every transaction is usually based on their average sale. Many retail merchants still set a minimum $ amount for credit card acceptance but that is usually in violation of their contract with the credit card processor especially at the B&M retail store level but of course customers rarely complain.
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