Good day, I got married to my wife 4 months ago. But when she filed for her 2012 tax return 2 months ago, on her w2 she filed single because she can

If you married in 2012, it is best for your immigration case that you file a joint return with you wife. If you married in 2013, your wife would of course file by herself as single. If you are in the former situation, you may wish to talk to an accountant as to whether you will be able to file an amended tax return and apply for your individual taxpayer identification number (ITIN) at the same time. The ITIN is not a Social Security number and does not give you legal status in the States, but it is a way by which many individuals can legally pay their taxes in this country. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.

I would file an amended return claiming married filing separately.  It is not correct that she is single and you shouldn't file an incorrect return.  Give the amended return to the immigration service in support of the I-864.