If your wife has a social security number then yes you can file as Married filing joint and claim the EIC.  IF she does not have a social security number then no you can not file as married filing joint, you will need to file as single if you have no other dependents and cl;aim the EIC for your self.  If you have other dependents then you may be able to file as Head of Household.

Yes she does have a SSN. Every time I enter in the Turbo tax and on the question if we lived in the US for more than 6 month my answer is no and the question does not differentiate if she or I. It only ask if both. Turbo tax does not allow the credit.  

That is correct, both parties have to have lived in the U.S. for the entire year in order to qualify for the credit.

So should I do Head of household and have her do a separate return to be able to get the credit? 

The Turbotax program should walk you through the questions to determine if you should file as Married or Head of Household.  Basically did she live with you during the last six months of the year?