The United States never joined the League.
The League of Nations was the brainchild of Woodrow Wilson. The treaty for the League was defeated by isolationist Republicans of that era. The League failed in great part because the European colonial powers saw it as a mechanism for parceling out the world for their own economic gain. We're talking about England, France, Italy, the Netherlands for the most part. In 1932 the League failed because The Japanese wanted their cut. They had fought on the Allied side and felt that their ambitions in China, Korea and the Indonesian island chain weren't being supported by the League. Indeed the Japanese Ambassador used poker terminology to describe the Japanese displeasure. He said that the Western Powers had invited the Japanese to sit down at the poker table and then had changed the rules! Our foreign policy during the interregnum from WWI to WWII sucked.