You can enter it as a business expense if the card is only used for business purposes.
If you use it for personal purchases, you would need to prorate the business portion.
The personal portion would not be deductible.
The annual fee is really interest in disguise.
I would enter it as "Credit card, loan, and other interest".
According to the IRS as you point out:
"You can generally deduct as a business expense all interest you pay or accrue during the tax year on debts related to your trade or business. Interest relates to your trade or business if you use the proceeds of the loan for a trade or business expense. It does not matter what type of property secures the loan. You can deduct interest on a debt only if you meet all the following requirements.
You are legally liable for that debt.
Both you and the lender intend that the debt be repaid.
You and the lender have a true debtor-creditor relationship."
A credit card in the business name would suffice these requirements.
