Numerical codes for electromagnetic wave propagation in magnetized plasmas are mainly based on frequency-domain asymptotic methods, which provide a fast solution and are thus valuable for experiment design and control applications. However, in several cases of practical interest (e.g. mode conversion), these tools run close to their limits of validity and should be compared to full-wave solutions. The code RFFW solves Maxwell's equations with the finite-difference time-domain method in 3D geometry, for scenarios involving high-frequency waves with arbitrary electric field spectrum in plasmas with axisymmetric equilibrium. In fusion-related problems, the code may conduct investigations of wave propagation and absorption relevant to auxiliary plasma heating and current drive, reflectometry and instability control. The code has been parallelized with a hybrid OpenMP-MPI scheme, which has allowed exploiting the much larger processing power and memory of current-day supercomputers. In this work, we present the main aspects of the physics implemented in the code, and also refer shortly to the parallelization scheme. Furthermore, we show results that exhibit the strong scaling performance of the code, and examine cases of electron-cyclotron heating application in medium-sized tokamaks.