Generally, no. You can take your ex to family court and ask that the family court order her to sign the form, or hold her in contempt. But the IRS will not honor the agreement without the signed form.
The only exception is if the divorce was signed before 2009, and if it contains specific language stating three things.
1.the years when you are entitled to claim the dependent.
2.that she will not claim the child in those years.
3.you're right to clean the dependent cannot to be contingent on any outside factors, such as being current with child support payments. You must have an unrestricted right to claim the child.
If your divorce decree meets these requirements in terms of language and years that it was signed. Then you can attach a copy of the divorce decree to your tax return instead of form 8332.
