1099-R has my SSN in Payer's ITIN number and a different number in recipient. TurboTax says ITIN cannot be SSN. Can you please help to enter correctly?

Do you have a 1099-R from the same company for a prior year? You can look back at your records. You can also call the company and ask for their TIN.

I think they reversed the numbers. There’s an ITIN in recipient and my SSN in payer.  Is this possible?

Yes, it certainly appears this type error is possible (since it happened to you).

When you enter the 1099-R, make sure you put the numbers in the right fields,  with you as the Recipient and the issuer as the Payer. Failure to do so may result in review or e-filing errors.