I am on H1b visa and my wife is on F1 visa. We both SSN number. Can we file income tax jointly?

[abpatil]

I am on H1b since October 2015. Before that I was on F1 visa since Sept 2012. My wife is on F1 visa since August 2016. Before that she was on H4 visa. She also has SSN number and she had less than 10k income.
 
For year 2016 can we file taxes as Married Filing Jointly?

[LinaJ2018]

Yes, you can file Married Filing Jointly. 

As you are considered as a US resident for tax purposes, in order to file a MFJ, you will need to make an election to treat your nonresident as a resident.  See instructions  Nonresident to resident

With this declaration, you cannot e-file. You can still use TurboTax program to prepare all your tax forms, then print them out and submit by mail along with your declaration to the designated IRS address on your print-outs. 

[PriyeshShah]

What needs to be done if non-resident spouse does not require to pay Social Security and Medicare tax.?

How to make sure those taxes are not applied on non-resident spouse's income?

Does turbotax take care of it by itself?

[KarenJ2]

@PriyeshShah  You and your spouse are treated, for federal income tax purposes, as U.S residents for all tax years that the choice is in effect. However, for Social Security and Medicare tax withholding purposes, the nonresident alien may still be treated as a nonresident alien. Refer to Aliens Employed in the U.S. – Social Security Taxes.