First, we should understand that the cause of the US rejection of the League of Nations had more to do with American domestic politics than it had to do with world politics.  The US rejected the League of Nations largely because it did not want to give up any of its sovereignty.  This could be connected to world politics because the US had recently gotten involved in World War I and was worried about being pulled into another foreign war.  However, it had more to do with domestic politics.  Many people were not comfortable with the idea that the League of Nations might be able to tell the US that it had to participate in a war.  Therefore, they rejected the League.

The US rejection of the League certainly had a major impact on world politics.  This was because one of the richest, strongest, and most important countries in the world was not a part of the League.  The US was not the superpower it became after WWII, but it was clearly a very important country.  When a major power is not part of a world organization, that organization loses some of its credibility.  There are historians who argue that the League of Nations would have been much more powerful and effective if the US had been a member.

Thus, the US rejected the League of Nations largely for domestic political reasons, but its rejection of the League had an important impact on world politics.