According to the United States Census Bureau, the town has a total area of 2.2 square miles (5.7 km²), of which, 1.4 square miles (3.5 km²) of it is land and 0.8 square miles (2.2 km²) of it (38.36%) is water.
There were 707 households out of which 18.2% had children under the age of 18 living with them, 51.5% were married couples living together, 7.1% had a female householder with no husband present, and 37.8% were non-families. 32.1% of all households were made up of individuals and 16.3% had someone living alone who was 65 years of age or older. The average household size was 2.20 and the average family size was 2.77.
In the town the population was spread out with 18.8% under the age of 18, 5.4% from 18 to 24, 21.3% from 25 to 44, 28.0% from 45 to 64, and 26.5% who were 65 years of age or older. The median age was 49 years. For every 100 females there were 106.0 males. For every 100 females age 18 and over, there were 105.0 males.
The median income for a household in the town was $26,857, and the median income for a family was $30,417. Males had a median income of $25,486 versus $18,750 for females. The per capita income for the town was $15,456. About 11.2% of families and 15.4% of the population were below the poverty line, including 19.8% of those under age 18 and 8.6% of those age 65 or over.
Pupils are served by the Little Bay Primary School (Rockport, Pre-K-K), Live Oak 1-3 Learning Center (Rockport), Fulton 4-5 Learning Center (Fulton), Rockport-Fulton Middle School (Rockport), and Rockport-Fulton High School (Rockport).
The city is also served by the Aransas County Public Library. The library is located in Rockport.