French people will understand this sentence if the context is well established, and if it is obvious that we speak of fear. But it’s not natural and no one says that without completing the phrase “Cette coutume me glace le sang”, “Cette coutume à de quoi glacer le sang”.

As @Doubidou said, it will be understood in a well defined context, but I have never heard it and would not say it.

If you really want to avoid saying “le sang”, then you can use “glaçant”, as in :

Le récit est glaçant

A quick research on Google with glaçant only points out to murder stories and such, so the context is quite clear on its own.