Normally when stepping down so much (1/4 of the input voltage in this case), you'd use a buck converter for efficiency. However, since your load only draws 7.7 mA, the dissipation in a simple linear regulator is only 70 mW. Even something as small as a SOT23 package can handle that without issue, assuming your operating at normal room temperature.
There are lots and lots linear regulators out there. 3V is a common enough voltage that you should be able to find one fixed at that voltage, like a 7803 and many others. The thing to watch out for is to make sure the regulator you get can handle the 12V in. Some LDOs (Low DropOut) regulators work only with lower voltages. Also pay attention to what the datasheet says about caps the regulator might need on its input and output. Without the right caps, it could oscillate.