Conformal slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds are introduced. We give a non-trivial example of proper conformal slant Riemannian maps, obtain conditions for certain distributions to be integrable and find totally geodesicity conditions for leaves of distributions. We adjust the notion of pluriharmonicity by considering distributions on the total manifold of a conformal slant Riemannian map, and get conditions for such maps to be horizontally homothetic maps. © 2022, Bayram Sahin. All rights reserved.