Get your taxes done using TurboTax

If you make the election to treat yourself as a full-year Resident, you can file your tax return as Married Filing Jointly.  However, that means you need to enter all of your Worldwide income for the entire year on your US tax return.
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If you do that, you fill out your W-4 that you give your employer just like it instructs you to do.  Just follow the worksheet on the top of the W-4, and you should probably be okay.