We consider a stochastic integral equation in $\mathbf{R}^n$, i.e. integral equation to which a stochastic perturbation is added. In the first place we consider the linear equation with constant coefficients. For this equation, first of all, we establish the uniform boundedness of the solution and, by using this uniform boundedness and by considering the solution in a suitable Hilbert space, we prove the existence of an invariant measure for this equation; the invariant measure will be proved to be unique. In the second place we consider the non-linear equation with suitable conditions and, by using a method developed for the linear equation, we prove the existence of an invariant measure for this non-linear equation.