The Social Security program began in 1935 when President Franklin D. Roosevelt signed the bill into law. This post includes a photo of the bill signing ceremony and a YouTube video so you can listen to FDR’s remarks that day.

FDR signing the Social Security Act

Listen to FDR’s remarks on YouTube.

We put those payroll contributions there so as to give the contributors a legal, moral, and political right to collect their pensions and their unemployment benefits. With those taxes in there, no damn politician can ever scrap my social security program.
President Franklin D. Roosevelt, 1941

If you want more details on the history of Social Security, there’s a good article on Wikipedia.