I recently read online that it does have an effect, called "binding". That means that Congress is obliged not to pass any law, or a successor President not to do any thing, that contravenes the treaty, until such time as the Senate votes the treaty up or down.
It turns out Clinton did that several times, on purpose, to screw with us; and his 'Rats in Congress kept the treaties (Kyoto, LOST) from coming to a vote, precisely to keep Republicans in a "bind". That's why George W. Bush publicly denounced Clinton's signature on the International Criminal Court treaty, to get the U.S. out of the "bind" that Clinton had placed USG under, in his scuzzy snakiness and 'Rat-nasty machinations.
Politically binding, perhaps, but not legally so.