In most cases it is better for a married couple to choose Married Filing Jointly filing status, even if one spouse had little or no income. This allows you the possibility of claiming several tax credits that are disallowed to Married Filing Separately filers. In addition, you benefit from the higher $12,600 Standard Deduction and both (your and your wife's) $4,050 Personal Exemptions.
Amend your return, making reference to TurboTax Guide - Amending Your Income Tax Return. File the Form 1040X and attachments using the procedure described below.
Your question does not make clear whether your wife is a resident alien or non-resident alien. If she is a resident alien, you may use Married Filing Jointly status, by right. If your wife is a non-resident alien, you may choose to take advantage of Married Filing Jointly status, but certain conditions apply. More detail can be obtained here: IRS Guidance on Filing with Nonresident Spouse.
Since your wife does not have a Social Security Number, she will need to request an Individual Taxpayer Identification Number (ITIN) using Form W-7. To apply, follow this link: Application for IRS Individual Taxpayer Identification Number.
If your wife is a non-resident alien, you will have to file your completed amended tax return by mail, along with Form W-7, and include a written statement signed by both of you, declaring that one spouse was a nonresident alien and the other spouse a U.S. citizen or resident alien on the last day of your tax year, and that she chooses to be treated as U.S. resident for the entire tax year.
Because you are filing your amended tax return as an attachment to your ITIN application, you should not mail your return to the address listed in the Form 1040X instructions. Instead, send your return, Form W-7 and proof of identity and foreign status documents to:
Internal Revenue Service
Austin Service Center
P.O. Box 149342
Austin, TX 78714-9342