Sometimes we do not connect a resistor inline with the capacitor. Or, we might charge the capacitor through one impedance, then discharge it through another impedance.
An RC network creates time dependent behavior. The RC time constant is a figure which determines the timeframe for charge/ discharge action.
The RC network itself does not create resonant behavior. If you add an inductor to the network, that can create resonant behavior.
Or there is a way to make an RC network create oscillations, if you add the necessary components around it.