NO you cannot add  a 2020 form 8606 to a 2021 return ... you must file the 2020 form 8606 now.  Good thing is you can simply complete and file this form by itself. 

https://www.irs.gov/forms-pubs/about-form-8606

Can I file it via TurboTax or you recommend mailing it directly to IRS?

TurboTax won't file  Form 8606 by itself.

TurboTax will give you one e-Filed amended return if you e-Filed Form 1040.

You can do an amended return to add Form 8606 and e-File it.