This paper presents a method for the homogeneous stabilization of homogeneous driftless input-affine systems using feedback controllers with Wiener processes. Although previous studies have shown methods for the stabilization of nonholonomic systems by using Wiener processes, the closed-loop systems sometimes show slow convergence. To improve the convergence rate, we show a method that gives a homogeneous controller by redesigning the controllers designed by the previous methods. By the virtue of the homogeneity, the closed-loop systems exhibit almost sure exponential stability with respect to homogeneous norms. A numerical example shows the effectiveness of the proposed method.