No, he never said this.
It's unclear where this aphorism originated, but there's no evidence it was Einstein. It does not appear in the comprehensive collection of quotations “The Ultimate Quotable Einstein” from Princeton University Press and it's quite unlike anything he's known to have said.
Throughout his career, Einstein did not concern himself with trying to make members of the general populace feel "special", but instead focussed on increasing our understanding of the universe.
Aside from that, there is no logic to this aphorism. It attempts to argue that everyone is a "genius" in some capacity, but that is not the case by any widely accepted definition of the word...
By the standard definition, a genius is someone who possesses an "exceptional human trait", especially in the arts or sciences. Arguing that everyone is "exceptional" (or "special") is something you're more likely to find on Sesame Street.
A few more things Einstein never said:
“Insanity is doing the same thing over and over and expecting different results.” - Original author unknown Source
"Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it." - Originally from an advert Source
"Only two things are infinite: the universe and human stupidity, and I'm not sure about the former." - Probably not, but there is some evidence Source
More things Einstein didn't say.