As shown in a schematic diagram below, this circuit implementation of phase shifter circuit  is well suited to using digital potentiometer  to control the resistive control element of  the phase shifter.

Digitally Controlled Phase Shifter circuit schematic

The phase at a given frequency is now under control of a digital signal using this circuit which is optimized for phase-shifting over the audio range. By using a single digital control line, the DS1669 used here can have its wiper position set to cause the wiper position increment upon each low-going pulse, until it reaches the upper end of the pot, when it will reverse direction and decrement.To cause the phase constantly sweep (an effect commonly used in popular recordings today), we can supply a clock to this digital control input. The digital potentiometer is biased at 1/2 VCC since this is a single supply circuit. [Circuit’s schematic diagram source: maxim-ic.com]