Why does a capacitor create a 90 degree phase shift of voltage and current?
If, instead of a sine-wave, you consider a turning on the circuit for the first time, with a DC voltage source and a discharged capacitor.

Immediately after you turn on, the maximum current will be flowing, and the minimum voltage will be across the capacitor.

As you wait, the current will reduce as the capacitor charges up, but the voltage will increase.

As the voltage arrives at its maximum, the current will have reached minimum.

And that's basically it - that's a description of a pair of sine-waves (one voltage, one current), 90 degrees out of phase, with alternating mutually-exclusive minima and maxima.