Is there a way to give root privileges to an app through the ADB?
Nope. Though you could use e.g. pm grant and grant it SUPERUSER, but that would have no effect if the app hadn't declared that in its manifest. And if it had, it wouldn't be necessary to grant it manually.

An app must actively request superuser privileges in order to gain it – and even then it only works with a superuser app in place (acting as "gate keeper") that then pops up a message for the user to confirm.