No, there is currently no toll for crossing the Dauphin Island Bridge (the Gordon Persons Bridge) via State Route 193. The bridge has been toll-free for many decades. Historical records show that when the original bridge opened in 1955, there was a toll, but that toll was discontinued in 1963.
If you want to read more about how the bridge was funded, its construction, and its development over time (including when the toll was phased out), see our post: Dauphin Island Bridge: History.