Tailoring the ion energy distribution function (IEDF) is vital for advanced plasma processing applications. Capacitively coupled plasma (CCP) discharges excited using a non-sinusoidal waveform have shown its capability to control IEDF through the generation of plasma asymmetry and DC self-bias. In this paper, we performed a particle-in-cell simulation study to investigate the IEDF in a symmetric capacitive discharge excited by a saw-tooth-like current waveform at a very high frequency. At a constant driving frequency of 27.12 MHz, the simulation results predict that the ion energy asymmetry in the discharge scales with the discharge current amplitude. A transition from a single narrow ion energy peak to a bi-modal type IEDF is observed with an increase in the current density amplitude. Further studies at a constant current density and varying the fundamental excitation frequency show that the ion energy asymmetry enhances with a reduction in the driving frequency. Increase in the plasma asymmetry and significant DC self-bias at a lower driving frequency is observed to be one of the principal factors responsible for the observed asymmetry in the ion energy peaks. An investigation of DC self-bias and plasma potential confirms that the powered electrode energy peak corresponds to the DC self-bias with respect to the plasma potential, and the grounded electrode peak corresponds to the plasma potential. These results suggest that although lower driving frequency is beneficial for generating the discharge asymmetry and large DC self-bias, a narrow low energy IEDF is plausible in very high frequency driven CCP systems.