Many Bible teachers have tried to find America in the prophecies of the Bible. Some have included America with the "young lions" of Ezekiel 38:13 who weakly protest the spoiling of Israel or in the reference in Ezekiel 39:6 to "them that dwell carelessly in the isles." Others have seen America in the first of the four great beasts in the vision in Daniel 7.
Daniel 7:4 - "The first was like a lion, and had eagle's wings: I beheld till the wings thereof were plucked, and it was lifted up from the earth, and made stand upon the feet as a man, and a man's heart was given to it."
The lion is supposed to represent Britain and the eagle's wings America. The plucking of the wings represent the diminishing of the power of America to a place of inconsequence. Though I find this interpretation compelling, I am not confident that it is definitely a reference to America.
Specifically, you ask about the United States being mentioned in the Book of Revelation. I do not know of any clear reference. In Revelation during the time of the tribulation, the antichrist is given power over the nations (Revelation 13:7), Babylon will make "all nations drink of the wine of the wrath of her fornication" (Revelation 14:8; 18:3), and the great whore who represents the false religion of the tribulation sits on the "peoples, and multitudes, and nations, and tongues" (Revelation 17:15). By the sorceries of Babylon "were all nations deceived" (Revelation 18:23). If the United States exists during this time, it will also be caught up in the perversions of the times as one of the nations.
I know that there are other places in the Bible that some claim refer to America, but I cannot think of them now. There is a speculation in all of these claims. However, one thing seems clear. The United States is not a major player in the events of the tribulation. We read about Europe, the Middle East, the Far East, and North Africa as places of importance in the books of prophecy. If the USA is there, it is evidently a minor player. Although the country could be destroyed before this time, that does not have to be the case. But it is certain that America is not the world power it is today. That should be a sobering thought to all who would put their hope in an earthly power. All nations and empires rise and eventually fall. America will be no different. Our hope is in God; not in the stars and stripes. I love my country, but I love my Lord much more. One is forever; the other is not.