Yes, in J.R.R. Tolkien's legendarium, Aragorn did marry Arwen, and they had a son. Aragorn II, also known as Elessar, was the heir of Isildur and the rightful heir to the throne of Gondor. Arwen Undómiel was an Elven princess, the daughter of Elrond, Lord of Rivendell.
Their love story is an essential part of "The Lord of the Rings" trilogy. Aragorn and Arwen's relationship faced challenges due to their different races (Aragorn was a Man, and Arwen was an Elf). Despite the obstacles, they remained devoted to each other. Arwen ultimately chose a mortal life to be with Aragorn, forsaking her Elven immortality.
After the defeat of Sauron and the restoration of the Kingdom of Gondor, Aragorn was crowned King, and he married Arwen. They ruled together as King and Queen of the Reunited Kingdom of Gondor and Arnor. The couple's son, Eldarion, succeeded Aragorn as the ruler of the Reunited Kingdom after his passing. Eldarion's descendants, through the line of the Kings of Gondor, continued the legacy of Aragorn and Arwen in Middle-earth.