When was the Social Security Trust Fund created?

Correct answer: 1939, as told by the official historian in 2005.  [Important Note!  This linked report is not about the trust fund itself, but how it was temporarily included in a Unified Budget with the rest of the US Government.  That practice began in 1969 and ended in 1983.]

Between 1935 and 1939, the surplus of Social Security was kept on the books of the US treasury, but not as a formalized entity.

I find this Official History to be very interesting, but if you don't already understand such things as how the Social Security system is primarily a pay as you go system, can remain that way forever, and that the contributions were raised 15% in 1983 following the recommendations of the Greenspan Commission to ensure the program would be solvent and able to pay all benefits 75 years into the future, you should read the Wikipedia description.  The Greenspan Commission recommendations were signed into law by Ronald Reagan.  Alan Greenspan was later appointed to be the Chair of the Federal Reserve by Reagan.

Here is the Greenspan Commission Recommendations.  Actually quite a few changes were recommended and made, but the biggest was that the contribution rates were raised from 5.4% to 6.2%

The Number One recommendation was not to alter the fundamental structure of the program.