My spouse filed our personal taxes jointly. How do I file my self-employment taxes on their own?

You can't.  It has to go on the Joint return.   You will have to amend your return to add your Schedule C.

You should not amend until the first return has fully processed and you get the first refund or your tax due payment has cleared.  

The 2021 1040X amended return won't be ready until March 17, 2022.  See this list

Federal Individual Forms Availability

Your self-employment taxes are automatically calculated and added to your tax return when you include Schedule C Profit or Loss from Business in your tax return.  If the joint return filed by your wife did not include your Schedule C you will have to add Schedule C,

If the return is rejected by the IRS you will fix the error that caused the rejection, add your Schedule C and efile the return.

If the return is accepted by the IRS you will have to amend the return to include your Schedule C.

 To enter your self-employment in TurboTax follow these steps:

1. Open or continue your return
2. Search for schedule c and click the Jump to link in the search results
3. Answer Yes to Did you have any self-employment income or expenses?
   • If you've already entered self-employment work and need to enter more, select Add another line of work
4. Follow the onscreen instructions

These links Where do I enter Schedule C? and How to amend (change or correct) a return you've already filed have information you may find useful.

Edited  [08/08/2020 | 5:08PM pst]