First Community Bank Rockport branch is located at Highway 35 North, Rockport, TX and has been serving Aransas county, Texas for over 6 years. Banking. Corpus Christi, Texas followers. First Community Bank is an to include banks in Kingsville, Portland, Padre Island, Rockport and Victoria with our. How can First Community Bank help you? Count on our friendly, knowledgeable staff to provide the best service in the Coastal Bend. Community Checking Plus.