4-20mA current loop simulator
Are you using a LOG or LINEAR pot?

EDIT:

This is for the linear pot:



Encircled in RED is your 10kOhm LINEAR potentiometer.

Resistance values may need a bit of tweaking.

EDIT2: this is an adjustable constant current source. Assuming the zener voltage is constant a constant current will flow through R1, R2, R3. The voltage on R1 will thus also be constant. This means the wiper of the potentiometer will travel between two fixed potentials. As the potentiometer is linear, the wiper voltage wil also change in a linear in fashion in relation to the actuation of the potentiometer. On the potentiometer wiper you have the base of Q1, which forms an emitor follower with R5. this prevents loading of the potentiometer. The voltage drop accross the base - emitor junction is approx. constant (~0.7V), which means the voltage accross R5 is also linear with the potentiometer travel. For practical purposes all the current flowing through R5 flows out the collector of Q1 and ends up in a load, the 250 Ohm resistor for your Arduino testing.

And there you go, your linear current with linear potentiometer travel.