Most ATX supplies do not have any current limiting, only a short circuit protection for the current at the primary side.
It will not be accurate, but you can limit the output current by injecting a voltage into the voltage regulation loop:
You need to sense the current in the GND wire using a small current shunt (to avoid a high voltage drop) and amplifiy the signal. Then connect the voltage over a diode to the feedback pin of the control ic. This can be a TL431 or the often used TL494(=KA7500). Here it is pin 1 or 16 depending on the actual circuit. Whenever the amplified current signal goes above 2.5V, the output voltages will be reduced.
The current regulation can be improved with a proper current control loop, but it will be much more difficult than the crude modification I described.
Or simply buy a proper power supply with adjustable current limit. 1A is probably more than enough for most arduino projects.