Yes. There is a potential workaround if you are a U.S. Resident or Resident Alien. (For filing NonResident U.S. tax returns see the bottom of this post)
As you said, TurboTax does not directly support the filing of Form 1042-S. However, If you are required to file this form along with your tax return, you can use TurboTax and file a paper return and attach Form 1042-S manually.
Complete instructions for filing your income reported to you on Form 1042-S for tax year 2015, as well as descriptions of all income codes reported on this form, can be found at the following IRS site: https://www.irs.gov/pub/irs-pdf/i1042s.pdf
Sometimes, this form is mailed out strictly for informational purposes and therefore does not need to be included on your return. This is often the case when Resident Aliens receive this form.
The significant items on the 1042-S form are Box 7 and Box 10. Box 7 isUS Federal Tax Withheld and Box 10 is Withholding Credit. If both of those boxes are 0, then nothing was withheld and there is no withholding credit and the 1042-S form is just for your informational purposes.
If you are filing a NonResident U.S. tax return, you will also need to use the service provided at the following TTO FAQ link: https://ttlc.intuit.com/replies/4028799
