Does the curse of Ham refer to Black people?
First, it's important to read the biblical text! There is no "curse of Ham" in Genesis 9. Instead, Noah places a curse on Canaan (who in the narrative is Ham's son). And this "Canaan" is obviously the eponymous ancestor of the Canaanites of the land of Canaan, who are the ones the Israelites are subsequently depicted (in the book of Joshua) as depriving of the land, in punishment for their idolatry and wickedness, so the story goes.
The first appearance of a "curse of Ham" is in the Middle Ages, and it's a puzzle where it comes from, as there is no basis in the Genesis text.
Second, the figure Ham in Genesis 9 is the ancestor of the peoples of Canaan, and also Egypt, and perhaps Libya, and Ethiopia. So, by no means simply "black people." Only in the European period of colonialism did the idea appear that the curse of Canaan was transferred to Ham and justified slavery.
For a good discussion of the matter, see Ephraim Isaac, "Ham (Person)," The Anchor Bible Dictionary, 3:31-32.
The short answer is no, but let me expand.
The question is referring to Genesis 9:18-27 where, after the Great Flood, Noah gets drunk and Noah's son Ham enters Noah's tent and sees him naked. Noah then curses Ham's son, Canaan, saying he should be a slave to his brothers. Another person on this site asked a question specifically about why seeing Noah naked was such a big deal, and if you're interested in that part of the question, you can find a number of answers by fine scholars here: "What's the issue with Noah's son seeing him naked?"
But there is a more sinister reason that this short, ancient passage stays alive today, and that is because the passage has been used to prop up systems of racial superiority from ancient times right up to today as described in this New York Times article. While it is used most frequently by White Supremacists and other White Identity movements, it also has been used in other racial conflicts. Most notably it was used in the Rwandan genocide to justify pitting the indigenous Hutu and Tutsi peoples against each other.
If you would like to read more about the latter (including the role European colonialism played in making those racial distinctions in Rwanda) you can read Mirror to the Church: Resurrecting Faith after Genocide in Rwanda by Emmanuel A. Katongole. The Rwandan genocide should teach us to take seriously the threat posed by the use of the passage by White Identity movements today.
There are several things to note about the passage, and I'll try to present them simply here.
1. The reason people latch onto race here is that, in a literal interpretation* of the biblical account of the Great Flood, all life on earth is wiped out except for those on the ark. That makes Noah a kind of new Adam with all peoples tracing a lineage back to Noah and one of his three sons: Ham, Shem, and Japheth. The Hebrew translation of the names of the sons have colors associated with them (sometimes very loosely), so those who take the Bible literally assign each of the sons as the ancestor of people with different skin colors. This is amplified by various biblical listings of nations that came from one of the three brothers. Since both the Egyptians and Ethiopians are in the biblical record as being descended from Ham, he has been seen by literalists as the ancestor of Black people across the globe.
2. But if you want to get literal about the text, it is Ham's son Canaan and not Ham who is cursed; and it is Noah and not God who curses Canaan. In fact, God blesses all three of Noah's sons in Genesis 9:1 and then creates a covenant with them, their descendants, and all the living things of the earth in Genesis 9:9. Nowhere either here or elsewhere in the Bible does God take that blessing away. God's blessing overrides Noah's curse, even in a literal reading. That universal blessing is confirmed later in the story of Abraham where God tells Abraham, "in you all the families of the earth shall be blessed." (Gen 12:3) The inherent equality of all is also affirmed by St. Paul in Galatians 3:28 "There is no longer Jew or Greek, there is no longer slave or free, there is no longer male and female, for all of you are one in Christ Jesus."
3. The term "race" as we use it today is unknown in the Bible. The only times that word is used in the King James version of the Bible is to refer to a foot race. In newer translations you find the English word "race" referring to the human race when the underlying Greek or Hebrew word means "human" but older translations had used the inaccurate word "man" to refer to both women and men. In other translations you find the English word "race" used in places like 1 Peter 2:9 to refer to a "chosen race," but the underlying word in Greek in those instances is about family and kinship, not race as we define it today. Race based on skin color simply is not a biblical concept and the notion that the Bible labels one race as superior to another is even further off the mark. It is a harmful misreading and misunderstanding of the biblical text.
4. The story of Noah and his sons was told orally for thousands of years before being written down. Underwater archaeologist Robert Ballard believes a great flood hit the region around 5,000 BCE which could mean that the story was first told even before writing was invented (which happened about 3,000 BCE). Even the most conservative beliefs about the writing of the Book of Genesis put it around 1400 BCE, which is also close to the time that some believe the Israelites under Joshua started their wars on Canaanite cities and towns.
As the answers to the other question about this text show, most scholars believe that the curse on Canaan (who the Bible lists as the ancestor of the Canaanite people) was added to the story as a way to justify the wars against the Canaanites by the ancient Israelites described in the book of Joshua.
5. Using biblical stories to justify our own desires is as old as the biblical texts themselves; and we are not immune to that temptation today any more than they were back then. The Rev. Dr. Martin Luther King, Jr. called the attempt to use the curse of Ham as an excuse for racism and slavery "a blasphemy" that "is against everything that the christian religion stands for." Here at the Massachusetts Bible Society, we agree with Dr. King's assessment and condemn strongly and unequivocally the use of the Bible as a prop for racial supremacy.
Some of these same points as well as others are made in an excellent post by Eliza Thomas, which you can read here.
*We at the Massachusetts Bible Society do not believe the Bible is meant to be taken literally. You can read our Statement on Scripture here and you can get my own book on the subject here. So, for the record, you won't be hearing from us that people across the earth have different skin colors because of Noah and his sons. But that literal interpretation is presented in responses like this because that kind of reading is the root of many of the questions asked on this site.