Can a DNA swab test tell me if I am Jewish? Judaism is a religion and there is no test that says one person is Jewish and another is not. There are tests however that check for similarities between your DNA and the DNA of people with Jewish ancestry or possibly a Cohen.
There are also certain markers that point to possible links to the Cohanim, the priestly tribe of Judaism. The most common test is to see if a male carries the marker, which is also carried by a large amount of Cohanim (priests, also written as Kohanim). This test checks the Y chromosomes which are passed from father to son and can point to the possibility that a male ancestor was descended from Aaron, the first High Priest and brother of Moses. This test does not determine religion, because according to Orthodox and Conservative Judaism, religion is passed from mother to child, not from father to child. Reform Judaism has a different approach and also looks at patralineal descent. If the mother is Jewish and you carry the marker then it points to the fact that you are likely a Cohen (priest) although somewhere along the way the transmission may have been interrupted despite that one carries the marker.