If the debt was incurred during your marriage, there is nothing you can do this year. Next year, you would need to file as married filing separately. But this will likely disqualify you from some important deductions or credits.
If the debt was incurred before the marriage, your spouse can file an "injured spouse" form. This is under the "Other tax situations" heading. The form can be filed alone, after the refund is paid, and asks the IRS to reconsider based on the fact that this is your debt but your spouse had most of the income. Your spouse prepares the form under her name and SSN, signs it, and mails it to the address listed.