Scattering of ion cyclotron range of frequency (ICRF) waves by plasma density perturbations in the edge has been previously studied with the help of antenna code RAPLICASOL (2020, Nucl. Fusion, 60, 096001). The further interesting question is whether the density perturbations have an effect on ion cyclotron resonance heating (ICRH) in the core. In this paper, FEM based 2D full wave code integrating the core with edge is used to study this issue. The analytical density perturbations are applied to study the influence of density perturbations on field distribution, power deposition, waves coupling and power partition among different species in the core and the fraction of energy dissipation in SOL. The influence of density perturbations becomes global and significant when the poloidal size of the density blob is comparable to the perpendicular wavelength. In addition, the amplitude and the radial size of the density blob are positively related to the strength of waves scattering. Finally, a typical experiment on EAST is chosen and the influence of realistic density perturbations on ICRH is evaluated.