It tends to relax as time goes on with the weight of the necklace itself.
You might be able to try unrolling it from the card or what not as it was packaged, using a binder clip or clothes pin to hold one end on something tall. Next get a spray bottle with water, and lightly mist the cord the whole way down. Make sure you either weight the tail or keep running your hand down it to keep it straight. Let it dry with a weight on it so it stays straight.
Or, if you don't want to try misting it, you could put it in the bathroom as you shower for a couple of days. The moist air might permeate it as well to help straighten it.
A light water mist won't damage leather, but it does make it more flexible. People who do leather working have to do it before tooling the leather, or it would be really hard to get a good solid mark down.
Best of luck! I keep replacing the leather every couple of years on my necklace that I wear every day. It tends to be kind of stiff for the first few days, then the kinks work their way out.
(I stick with leather so it will break away if it gets caught on something at work.)