The most commonly used method is to put a 250 Ohm resistor in the current loop; the voltage drop over the resistor gives you a 1 .. 5V output signal for 4 .. 20 mA, or 0 .. 5V for 0 .. 20 mA.

If the 1V loss is unacceptable, you will have to add some additional circuitry (basically an op-amp) to add a -1V offset and amplify by 1.25 An other option would be to use an A/D with a little higher resolution; it may be advantageous to be able to detect an open loop anyway so this might be worth some consideration.