Voltage regulator like LM 317 which can interface like SPI or I2C
One way to do this is to use a Electrically-Erasable Potentiometer, or EEPOT, in place of the variable resistor connected between the ADJ pin of the LM317 and ground.

For example, the Microchip MCP4162 comes in a rheostat (two pin) configuration with full-scale resistances of 5K, 10K, 50K and 100K ohms with 257 steps and an SPI interface. You can get one in either a DIP or surface mount package for about a dollar at Digi-Key.

There are also lots of EEPOTs with I²C interfaces.  Search for "digital pot" at Digi-Key.

If you select a different part, make sure it comes with non-volatile memory, so every time it powers up, the voltage will go back to the last setting.  Otherwise you would have to reset the value on each power-up.

Note: This suggestion only works if you have a separate source of power for the EEPOT, since you obviously can't power it off the LM317 as you are adjusting it.  But I assume this is the case, since you wouldn't have power to run your SPI or I²C either.