The Battle of San Jacinto was significant in American history because it led to the capture of President Santo Anna and led to Texas' victory in the Texan War of Independence.… In addition, the battle also led to Santa Anna being forced to sign a treaty that officially recognized Texas as an Independent country.he battle of San Jacinto happened in present-day Harris County, Texas. 9 people found this useful. Edit. Share to: Mark Swarthout. 775,933 Contributions. Contract attorney. When not working I teach karate, collect stamps, write books, and play the ukulele.