We will go out on a limb here and, even lacking firm evidence, based on his bio, we will say, no, Edward Snowden is not a Jew. Wikipedia says he, "listed Buddhism as his religion on a military recruitment form, noting that the choice of agnostic was 'strangely absent.'"
US News on NBC news reports: "Born June 21, 1983, he grew up in Wilmington, N.C., but later moved to Ellicott City, Md., he told The Guardian. His mother, Wendy, is the chief deputy clerk for administration and information technology at the federal court in Baltimore, a court official told NBC News. His father, Lonnie, is a former Coast Guard officer who lives in Pennsylvania, the Allentown Morning Call reported. A neighbor said he has an older sister who is an attorney."