  We establish the existence of infinitely many global and stationary solutions
in $C(\mathbb{R};C^{\vartheta})$ space for some $\vartheta>0$ to the three
dimensional Euler equations driven by an additive noise. The result is based on
a new stochastic version of the convex integration method, incorporating the
stochastic convex integration method developed in \cite{HZZ22b} and pathwise
estimates to derive uniform moment estimates independent of time.
