In the present work, essential oils (EOs) extracted from different parts of sour orange Citrus aurantium (green leaves/twigs, small branches, wooden branches, and branch bark) were studied through gas chromatography coupled with mass spectrometry (GC/MS). Furthermore, the EOs in the amounts of 5, 10, 15, 20, and 25 µL were studied for their antibacterial activity against three pathogenic bacteria, Agrobacterium tumefaciens, Dickeya solani, and Erwinia amylovora. The main EO compounds in the leaves/twigs were 4-terpineol (22.59%), D-limonene (16.67%), 4-carvomenthenol (12.84%), and linalool (7.82%). In small green branches, they were D-limonene (71.57%), dodecane (4.80%), oleic acid (2.72%), and trans-palmitoleic acid (2.62%), while in branch bark were D-limonene (54.61%), γ-terpinene (6.68%), dodecane (5.73%), and dimethyl anthranilate (3.13%), and in branch wood were D-limonene (38.13%), dimethyl anthranilate (8.13%), (-)-β-fenchol (6.83%), and dodecane (5.31%). At 25 µL, the EO from branches showed the highest activity against A. tumefaciens (IZ value of 17.66 mm), and leaves/twigs EO against D. solani and E. amylovora had an IZ value of 17.33 mm. It could be concluded for the first time that the wood and branch bark of C. aurantium are a source of phytochemicals, with D-limonene being the predominant compound in the EO, with potential antibacterial activities. The compounds identified in all the studied parts might be appropriate for many applications, such as antimicrobial agents, cosmetics, and pharmaceuticals.