Bode Phase Plot of RC High-Pass Filter
I know that from my engineering that voltage lags behind the current passing through the capacitor. So, I assume the current through capacitor will be in-phase with the input voltage waveform


I'm not clear how you went from the first sentence to the second one here.

If the voltage lags behind the current, then the current leads the voltage. In any case they are 90 degrees out of phase with each other, so assuming they are in phase is not what you should do.

Only at high frequencies, where the capacitor has very little effect on the circuit, will the current become very nearly in phase with the input voltage (which is applied across the RC combination, not just across the capacitor).  And this is exactly what your Bode plot shows.