120VAC Digital Potentiometer
There are at least a couple of different options but neither is going to be very good.

1) Use a LED / CdS cell combination.  The amount of LED current will change the CdS cell resistance  - typically from a few hundred Ohms all the way up to several Megohms.

The downsides are: a) Poor Linearity;  b) downright awful device-to-device matching.

2) Convert the dimmer design to a standard phase-control circuit using an appropriate opto-coupler (MOC3011).  The downside is that you need to sample the incoming AC zero-cross points and have your controller delay the signal into the opto by the correct amount for the particular dimming level desired.

Or: you could simply build or purchase a dimmer designed for remote control.  There are many existing designs available, ranging from analog control (0-10 Vdc) or a digital bit-stream or digital PWM control.