According to this article in the Tennessean,
Does a Cv-19 test detect the delta variant?
A viral test, either the nose or throat swab, can detect if you are positive for COVID-19. It’s not designed to tell you which variant you might be infected with, according to Human and Health Services of Texas.
Is there a test for the delta variant?
There is not a specific test for the delta variant.
However, since the vast majority of Cv-19 cases in the U.S. are the delta variant, it’s likely a positive test result indicates you could be infected with the delta variant, according to Human and Health Services of Texas.
You might wonder how then can they claim “the vast majority of Cv-19 cases in the U.S. are the delta variant”.
This fraud was backed up by someone in Australia who called a pathology centre to find out and got the same response — there is no such distinguishing test, only a positive or negative for Cv, period.