Yes, you can use the same TaxJar API Token for multiple Wordpress sites. There are some considerations though.
The API Token is tied to your TaxJar account and the nexus configuration of states. So if you are collecting sales taxes in the same states for all WooCommerce sites you should be fine. (If your different WooCommerce sites have different nexus (ie: collecting in differing states), you would need a separate TaxJar account for each site to have unique API Tokens.)