Conformally Stäckel manifolds can be characterized as the class of n-dimensional pseudo-Riemannian manifolds .M; G/ on which the Hamilton-Jacobi equation G.ru; ru/ D 0 for null geodesics and the Laplace equation G D 0 are solvable by R-separation of variables. In the particular case in which the metric has Riemannian signature, they provide explicit examples of metrics admitting a set of n 1 commuting conformal symmetry operators for the Laplace-Beltrami operator G . In this paper, we solve the anisotropic Calderón problem on compact 3-dimensional Riemannian manifolds with boundary which are conformally Stäckel, that is we show that the metric of such manifolds is uniquely determined by the Dirichlet-to-Neumann map measured on the boundary of the manifold, up to diffeomorphims that preserve the boundary.