A GPU-accelerated Finite-Difference Time-Domain (FDTD) scheme for the simulation of radio-frequency (RF) wave propagation in a dynamic, magnetized plasma is presented. This work builds on well-established FDTD techniques with the inclusion of new time advancement equations for the plasma fluid density and temperature. The resulting FDTD formulation is suitable for the simulation of the time-dependent behaviour of an ionospheric plasma due to interaction with an RF wave and the excitation of plasma waves and instabilities. The stability criteria and the dependence of accuracy on the choice of simulation parameters are analyzed and found to depend on the choice of simulation grid parameters. It is demonstrated that accelerating the FDTD code using GPU technology yields significantly higher performance, with a dual-GPU implementation achieving a rate of node update almost two orders of magnitude faster than a serial implementation. Optimization techniques such as memory coalescence are demonstrated to have a significant effect on code performance. The results of numerical tests performed to validate the FDTD scheme are presented, with a good agreement achieved when the simulation results are compared to both the predictions of plasma theory and to the results of the Tech-X® VORPAL 4.2.2 software that was used as a benchmark.