Would I be able to claim my wife as a dependent on taxes? If so what are the rules on that?

If you are a U.S. citizen or resident alien, you can NEVER claim your spouse as a dependent.

What you CAN do is file jointly with her, allowing you to claim her personal exemption and DOUBLE the $5,150 standard deduction, for a joint standard deduction of $10,300.

If you are a non-resident alien, you MAY be able to claim your wife as a dependent. I would need to know your country of origin to tell for sure.