No, this is not true, although it's been repeated so often and for so long that many people still believe it, and -- like your uncle -- have used it to justify their prejudice against people of other races.
Noah, the Bible tells us, had three sons, each of whom (after the great flood) would become the founder of a number of nations or peoples. One of the sons, Ham, became the founder of some groups that settled in Africa, although most of his descendants settled elsewhere, including Babylonia and Assyria in the Middle East. (You can read the list of the nations that came from Noah's sons in Genesis 10.)
Because of a specific shameful act that occurred after the great flood, Noah pronounced a curse or judgment on one of Ham's sons, a man by the name of Canaan. The judgment was that Canaan and his descendants would become servants or slaves to his brothers and their descendants, and over time, this actually happened. But the curse was not on Ham; it was only on his son, Canaan (see Genesis 9:25). Nor was Canaan the founder of any African nation or race; his descendants settled only in the Middle East.
Racial prejudice is sin in the eyes of God, and the Bible should never be used to defend it. God created the whole human race, and Jesus Christ died to redeem people from every race. Remember: "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life" (John 3:16).