In this article, we investigate the behavior of Ricci solitons under $D$-isometric deformations on a class of Riemannian manifolds. A $D$-isometry is a diffeomorphism that preserves the distance function induced by a Riemannian metric up to a constant factor. We consider a family of Riemannian metrics $g$ on a manifold $M$ that are related by $D$-isometric deformations, and we study the Ricci soliton equation on each metric $g$. We show that under certain conditions on the deformation function, the solutions to the Ricci soliton equation on each metric $g$ are invariant. In particular, we obtain a family of Ricci solitons that are related by a scaling factor under $D$-isometric deformations. We also provide explicit examples of $D$-isometric deformations and compute the corresponding Ricci solitons.