How does the resistance-capacitance oscillator shift voltage by 180 degrees?
You are correct that a capacitor &quot;shifts phase for current, not voltage&quot; or more accurately, the current in a capacitor is out of phase with the voltage. If the capcitor were ideal, the phase difference would be \$90^{\circ}\$.
However, the phase shift network in an RC phase shift oscillator does not consist only of capacitors, but also resistors.
If a voltage sine wave is applied to a capacitor and resistor connected in series, and an output voltage is measured across the resistor, there is a frequency dependant phase shift between the voltage across the resistor as compared to the voltage across the both components together. That phase shift, (for ideal components), lies between \$0^{\circ}\$ and \$90^{\circ}\$.
The reason for this voltage phase shift is that the current through the capacitor is out of phase with the voltage across it. This causes the current through the resistor to be out of phase with the voltage across both components. In turn, the current the resistor is in phase with the voltage across the resistor.
In your diagram, you have 3 RC phase shifters connected in series. Typically, phase shift networks are separated by amplifiers or buffers of some sort. The reason is that if the current through the capacitor is shared between a resistor and further circuitry, that further circuitry has an effect upon how the phase shift works. The further circuitry &quot;loads&quot; the phase shift network.
If the phase shift networks were identical, and separated by amplifiying or buffering circuitry, at the frequency where each network shifts the phase by \$60^{\circ}\$, their combined effect will be to shift the phase by \$180^{\circ}\$, providing an appropriate phase shift for an oscillator.