Can I pay off my personal credit card through the company I work for?
The ideal situation is to run this through payroll coded as bonus or whatever it is for and then you personally deposit the net of the check and personally pay off the credit card. It provides the cleanest audit trail.
The same thing is true if you're using the net check to pay for a student loan. Any time a business pays for personal expenditures, it is taxable income to the person receiving the "benefit" of that payment.
If the charges on the credit card were for business, then the business can pay off the credit card and code the expenditure to the appropriate type of business expense. Ensure you have the business receipts to back up the charges.
I would advise you to ensure your tax preparer is aware of this transaction to ensure proper attention for business and personal reasons.