Which one? There are several. The (fairly) new fishing pier/breakwater at the end of Market Street is nice, and lit at night. The seawall in front of the aquarium holds fish. The breakwater at the south end of the Rockport Marina is O.K. The pier north of the marina is a good fishing spot. All those are free. The fishing pier in Fulton, the two Copano Bay piers(formerly the old bridge, and Goose Island State Park have nominal fees, but are good spots.
Winter fishing is pretty good in Rockport.
I'm an Eighth Day Adventist. On the Eighth Day, God went fishing!