For 2016 what you should have done is filled out a W-7 application, enclosed the required documentation, print your tax return, and mail them all to the IRS. That would probably have gotten you the dependent exemption assuming you filed before the April 15 deadline.
I think that in this case, since you are already a US taxpayer and have your own tax number, you can submit just the form W-7 for your dependent without attaching it to a new tax return. It can't hurt to try, the worst they can do is send it back.
If they do send it back, then you should plan on submitting it for 2017 by printing the W-7 and the tax return and mail them together instead of e-filing.
