Electronic – LM317 µA Constant Current source possibility

note: question was originally about a current limiter

The LM317 with the single series resistor between output and adjust input is actually a fixed current source, not a current limiter. You don't need the LM317 to create a current limiter, a few discrete components will do:

For a limiting at 2mA you select a 330\$\Omega\$ resistor for \$R_{SENSE}\$. If there flows 2mA through it Q2 will start to conduct and reduce the base voltage of Q1, so that its current is cut off.

edit (re changed question)
Maybe you're focusing too much on the LM317. If you need a constant current you could use the LM234 which is a programmable current source for up to 10mA. You set the current with a resistor.

The point of the current limiter is that, if the current is higher than desired, it will reduce voltage, which with most Ohmic loads will reduce the current draw.

This uses the fact that voltage drop == resistance times current, and the regulator reduces voltage if it sees a voltage on the reference pin that is greater than the reference (1.2V? something like that)

Does this mean that the voltage out from the current limiter is at least 1.2V less than the input? Yes, it does!

However, if you have a microcontroller, and don't need "immediate" feedback (your uC response time is OK) then you can simply sample the voltage drop across a current sense resistor (something small like 0.1 Ohms) to estimate current, and drive any variable resistor, like a regular power transistor, using an analog output from your uC (or a filtered PWM.)

You probably want another solution, like an existing programmable potentiometer in the feedback loop of an opamp, for example. Use a current sense resistor that's small (0.1 Ohms?) and program the amplification of the voltage drop using an opamp. When amplification is 10x, then you get to 1.2 volts at 1.2 amps; when the amplification is 100x, then you get to 1.2 volts at 120 mA.