I am offered sign on bonus of 10000 USD.
Restrictions: I get 30% if I stay 13 months with my employer.
My Question: After taxes, I get around 7000K. If for some reason, I leave my employer before 13 months, I need to return all 10000, though I got only 7000 in hand.
How do I go about rest of the 3000, which I paid in taxes? Is there any procedure to get my 3000 back on tax returns?

The bonus IS taxable income, so you may not get it all back.

The $3,000 withholding will be reflected on your W-2.