I personally have not done this, but, yes, technically you can.
The chemistry stuff --
We use fats to make soap, because they are easily available to us. Fatty acids are not so easily available, but they also could be used just fine for soap making.
Speaking very generally, a fat molecule is made of 3 fatty acids bound together by a glycerine molecule. Oxidation (the process that causes rancidity) gradually breaks the fat molecule apart, ultimately into 3 fatty acids and 1 glycerine molecule.
If the hydrogen that makes a fatty acid ... a fatty acid ... is replaced by sodium or potassium, the fatty acid becomes soap.
Okay, now for the more practical stuff --
The goal is to make sure absolutely none of the fatty acids remain in the finished soap. One option would be to use a zero lye discount for a CP recipe. Another, possibly more effective method might be to HP your recipe using a slight amount of extra lye, then add enough "superfat" of good oil to ensure the lye is completely used up.
Be aware that the sodium hydroxide does not have to work very hard to saponify fatty acids, compared with the fat, so your recipe may trace quicker than expected. The lye calculation will be the same, however -- you need the same amount of lye to saponify rancid oil as you would to saponify non-rancid oil.
...speaking theoretically of course...
If any rancid odor remains in the finished soap, Ruthie is right -- your clothes may smell.