Mikhail Gorbachev? Not a Jew; although the amount of scapegoating he's taken from Russians over the years, we can make him an honorary member. Leonid Brezhnev? Definitely not a Jew (although incorrectly rumored to be married to one). But the man between them (and we will conveniently forget the useless Konstantin Chernenko, the William Henry Harrison of Soviet leaders), Yuri Andropov... is it possible?
This is where it gets murky. Andropov, who spent 15 years as the head of the KGB, kept falsifying his biography. In fact, Yuri might not even be his real name; it is potentially Grigory. The last name is opaque as well; Andropov was the name of his first stepfather. Who was his real father? Who the hell knows.
But it's his mother that draws the most of the attention, as she was the adopted daughter of Karl Fleckenstein, a Finnish jeweler who had a store in Moscow. (This apparently led to Andorpov's KGB handle, "Jeweler".) And that Fleckestein was apparently Jewish... which, off course, doesn't make Yuri Jewish himself.
So, no on Andropov. Unless there are even deeper secrets in that falsified biography?