There are a few ways to do this, each with their own issues. There are such things as "digital potentiometers". These act like pots with a large number of fixed set points, and the particular set point to use is controlled by sending digital commands, like over SPI or IIC. These are fairly common and available.
Why do you think you want to control the volume from a voltage instead of from a microcontroller? Where will the desired volume information ultimately originate from?
One issue with digital pots is that they are linear, and volume controls need to be logarithmic to get apparent constant volume change. This can be emulated by using a pot with a large number of taps and converting to log digitally. In that case you would have a micro with a A/D receive the desired volume voltage signal, convert that to a logarithmic scale, then send the resulting value to a digi-pot.
A long time ago before microcontrollers were accessible, I did a voltage controlled volume once by having the voltage control two LEDs oppositely. Each LED was optically connected to a CdS photoresistor. The two photoresistors were used as a light-variable voltage divider. Of course the result is quite non-linear in rather unpredictable ways. I was using it in a feedback loop to adjust the signal size of a oscillator, which otherwise inherently depended on frequency. With the feedback, it became largely independent of frequency. This was the same purpose Bill Hewlett used a light bulb for in his famous oscillator design.