That's already been ruled out by the SCOTUS. "Eleanor Roosevelt, Chairman of the United Nations Commission on Human Rights when the Declaration was drafted, spoke for the United States and stated that the Declaration "was not a treaty or international agreement and did not impose legal obligations; it was rather a statement of principles."
There is however the International Covenant on Civil and Political Rights, which is an international treaty. However, in practice, the ICCPR functions much like the UDHR - a statement of principles rather than a treaty which provides for proper enforcement. The US apparently specifically indicated when it ratified the ICCPR that it didn't consider the treaty "self-executing" as a matter of US domestic law and thus you can't enforce it directly in the US courts.
