"Its all this uncertainty with You-Know-Who coming back, people think they might be dead tomorrow, so they're rushing all sorts of decisions they'd normally take time over. It was the same last time he was powerful, people eloping left, right, and center ... Yes, well, your father and I were made for each other, what was the point in waiting?"
-- Molly Weasley (HBP5)
As Voldemort is becoming more powerful and life becomes more uncertain in the Wizarding World, many young couples, facing the uncertainty, get married quickly. Arthur and Molly, who had been sweethearts at Hogwarts, were one of these couples. When talking about it many years later, Molly noted that theirs was not a rash decision because of the war but because “they were made for each other.”
We don't know the exact date of their marriage, but since Molly describes it as happening during Voldemort's first rise to power in the 1970s, and since Bill was born in 1971, we're placing the date as approximately 1970.