A constant AC voltage will mean a Voltage Source, not a Current Source. Current sources maintain a constant current, with varying load voltage. A voltage source means a constant voltage, with varying load current. A series potentiometer will adjust the available current, but will also introduce a voltage drop of its own, and it will not be very precise. Also, depending on the current you plan to control, it may burn up. It would have to be rated for a high wattage.
Honestly, I'm not really sure what your teacher/boss/etc wants. A load will draw a specific amount of current, no more, no less. Having a variable current output really doesn't do anything. A 400mA device connected to a 400 amp supply will only draw 400mA. What would be the point of a variable current voltage source?
Matt