Let $A$ be a sheaf of commutative rings on a site $X$. (In my applications, $X$ comes from one of the standard Grothendieck topologies on algebraic varieties.) It should be true that $R\Gamma (X, A)$ has the structure of an $E_{\infty}$-algebra.

In my experience this fact is "obvious" to homotopy theorists, but I've never heard mention of a written reference that explains this fact. What is a suitable reference, if I want to use this in a formal writeup?