Romanticism was a literary movement in which authors and artists reacted to changes that occurred during the Industrial Revolution. During the Industrial Revolution, America became a hotspot of factory-led activity, and with it, population growth. Cities became overrun with people, and without modern advancements such as indoor plumbing and trash collection, they also became dirty and grimy. Romanticism was a reaction to this time period of industrial growth.
Romantics cherished nature above all else, and many of them were pulled to the wilderness of America. The wilderness was untouched by the current advancements and provided a reprieve from the dirt and overpopulation. Romantics believed in the self over society and valued intuition and emotion over logic and reason; they also believed in the importance of dreams, symbols, and the power of nature over mankind. Romantic texts usually had a romantic hero - someone who had rejected society's norms and whose life revolved around only himself.
Thinking of these characteristics, Moby Dick most definitely qualifies as a romantic text. Captain Ahab, the captain of the ill-fated ship, the Pequod, is driven by his own emotions in pursuing the giant while whale, Moby Dick. Logically, it's completely unreasonable to think he can locate one whale in the entire ocean, but he continues anyway. He puts a ship full of men in mortal danger in order to pursue his over vengeance. To him, Moby Dick is the embodiment of evil - again, an illogical idea. Captain Ahab is a Romantic hero - he has rejected his societal role and taken up this obsession with the white whale. Finally, nature (the whale) is successful in the end, triumphing over man.