  In this paper, we first construct a graded Lie algebra which characterizes
Rota-Baxter operators on an anti-flexible algebra as Maurer-Cartan elements.
Next, we study infinitesimal deformations of bimodules over anti-flexible
algebras. We also consider compatible Rota-Baxter operators on bimodules over
anti-flexible algebras. Finally, We define $\mathcal{ON}$-structures which give
rise to compatible Rota-Baxter operators and vice-versa.
