Although the League of Nations was much of the work of President Woodrow Wilson America never joined the League of Nations.
This was for several reasons, firstly America had suffered civilian casualties in the war, and many people in the USA wanted to keep America out of European affairs.
This policy was called isolationism and was probably the main reason that America didn't join the League.
Also joining the league meant that this might involve having to do things that might set back the economy or damage America otherwise.
For instance sending out soldiers out to other parts of the globe would be a very costly venture and there would probably be casualties as well.
There was also the fact that America had had little involvement in the war and had some civilians (especially German immigrants) also had little or no support for British or French policies and/or the Treaty of Versailles.
So although when the League was actually being formed Woodrow Wilson still backed America joining it, by this time America had had enough of wars and dealing with other countries problems and, despite Wilson America never joined the League.