Yes, you can.

You can use TurboTax Self-Employed, TurboTax Self-Employed Live, TurboTax Home & Business for Windows, and TurboTax Business to create W-2 and 1099-MISC forms for your employees and contractors.

If you're not using one of these versions to prepare your taxes, you can always use TurboTax Quick Employer Forms to e-file your W-2 and 1099s.

Instructions for TurboTax Self-Employed and TurboTax Self-Employed Live

Instructions for TurboTax Home & Business CD/Download software

Instructions for TurboTax Business

I'm not sure I trust what TurboTax says about their Quick Employer Forms.  If you enter data, it might disappear instead of being saved (as promised).

On about January 10, 2020, I (eventually) figured out how to enter payee data at the TurboTax web pages for eventual printing and eFiling of IRS Forms 1099-MISC (block 7, NEC Compensation) due tomorrow, January 31, 2020.  [For my 2019 returns, I upgraded to TTax Home & Business -- specifically because I wanted the advertised ability to eFile my 1099-MISC forms and know that my current 2019 data would be saved online for quick & easy transfer to next year.]

(1) It turned into a time-wasting hassle to (eventually) discover that the ability to enter 1099-MISC info via the online web pages could NOT be accessed from my freshly-created and therefore existing 2019 TTax file in my desktop computer. Instead, when first opening TTax I had to click the "Start a new return" button and from there choose to enter 1099-MISC (or W2, etc.) data. That worked and I manually entered data for about 30 payees. I chose not to eFile at that time (TTax FAQs explain that my data would be saved online for later eFiling and for transfer to next year). Instead of immediately eFiling, I opted to wait until the end of January (i.e., today, 01/30/2020) in case errors needed to be corrected before eFiling. [NOTE -- There was NO "sign out" link or button available on any of the screens that appeared for me, so I simply closed the browser window. Chrome browser.]

(2) Today, 01/30/2020, I am trying to get back to my previously-entered 1099-MISC data that is supposed to be stored someplace within my online account at TTax ... ... ... and, after successfully logging in with my username and password, I cannot find any of my previously-entered data. The option to enter brand new data appears, but NO saved data from a couple of weeks ago. AARRGGH! A link to previously-saved data does NOT appear when I use the "Start a new return" button when TTax first loads. I cannot find a link to my already-entered data when I go back into my already-started 2019 tax file that's stored in my desktop computer. AARRGGH!

Now I wonder why I wasted my time and money upgrading my TTax product so that I could (supposedly) enter and eFile 1099-MISC forms via TTax to the IRS.

The Windows  Desktop Home & Business program and the separate Business program can prepare them either way, Online using Quick Employer Forms -or- on your computer using the built in W2/1099 Reporter.  The Mac Desktop Home & Business program only has the online Quick Employer Forms.

In the Window's Home & Business Desktop program to Prepare W2s or 1099s, click the big blue button to Start a New Return or go up to File-New Tax Return.
Then on the next screen it asks What would you like to do?

If you get a screen with 2 choices, Check the second circle that says Prepare W-2s and 1099s for my employees or contractors.  Then that will expand and give you a choice to prepare them online or on your computer.