Artificial sinew will work for a bowstring, but it stretches A LOT! It will constantly be in a state of movement and will never really settle down unless made fairly thick, which is a whole other ball of wax. I used to use it when I first started building bows because I had a ton of it laying around. I was always adjusting the string to maintain brace height, and the bows just shot sloppy compared to a string made with less elastic materials.
But, if you've got it, it WILL make a string. It makes an especially fine historical replication.