Final answer:
Cysteine is the amino acid that can form a covalent disulfide bond with another cysteine, resulting in a cystine dimer and contributing to protein structure.
Step-by-step explanation:
The amino acid capable of forming a covalent bond with another of the same amino acid is cysteine. Cysteine contains a sulfhydryl (SH) group, which can react with another SH group in the presence of oxygen to form a disulfide bond (S-S bond). This unique feature allows two cysteines to create a dimer called cystine, significantly contributing to the tertiary and quaternary structures of proteins, such as the stabilizing links in insulin.