Since you can't claim the student loan interest deduction if you're married filing separately, then the only way to be able to take the deduction is to file an amended return (1040X) with both your wife & yourself on it. You'll check the status for married filing jointly and you'll both report all your income and deduction/credit information on the 1040X.
You'll need to wait until her original form has been processed and any refund issued. The IRS won't accept an amended return via e-file, so you'll have to print it, both of you sign it, and then mail it in.
Here's a link to the TurboTax support page for amended returns, which will get you started: https://turbotax.intuit.com/tax-tools/tax-tips/IRS-Tax-Return/Amending-Your-Income-Tax-Return/INF120...
