You need to file your own tax return and claim yourself. This will alert the IRS and when they question your ex he will lose the deduction and be charged penalties and interest.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.
If he forged your signature, you can report it:
If he claimed you as a dependent, the second they receive your return, they will scrutinize this other return that lists you as a dependent. He will have to explain this. He will not be able to.
Your fact pattern is missing a key fact about the timing of the divorce and the year for which he filed. That said, even if the divorce was finalized in for example march 2011, he could not file married filing jointly for 2010 without your signature. As the others stated, you have to file your own return. Because the timing is important it is to hard to be more specific.
Note, there are very specific rules on the use of a Social Security Number. The Social Security administration may take a complaint. In addition, you ex may be guilty of tax fraud. If you report him and it results in recover of taxes by the IRS, you could be entitled to up to 30% of the tax recovered.
I suggest you contact a taxpayer for assistance. You can also go to your local IRS office and they may be able to help you. If you believe your ex is using your social security number, contact the credit bureaus immediately to protect yourself.
The general advice above does not constitute an attorney-client relationship: you haven't hired me or my firm or given me confidential information by posting on this public forum, and my answer on this public forum does not constitute attorney-client advice
As indicated, if she files her own taxes, the problem should go away (for her). But, if she's serious about all the other allegations, then she could sue him in state court, get an order requiring him to sign a Form 4506 and find out the truth. She will have to make the effort, though. She could go to the police but that's a non-tax solution.
Filing complaints with the IRS or Social Security is possible, but will be cumbersome, too.