Turbo Tax says Form 1116 Foreign Tax Credit is not available. But the 2021 version of the form is available from the IRS.

That message is a little misleading. The form may be available from the IRS, but then it takes time to program, test and distribute the changes in the software -- hopefully soon. 

The hold-up is for the new "Schedule B" that accompanies Form 1116.  It is currently scheduled to be available on or around 3/31.  You can check for updates to that projected date here: TurboTax Forms Availability.  While not all taxpayers using Form 1116 will need this schedule, those who may will need to wait.  Form 1116 Schedule B also is not supported for e-filing this year.