Yes and no. Heart of Darkness could be called racist if you use today's understanding of racism and certainly, the way in which Conrad portrays the Africans in general leave us cringing. However, I think that the character of Marlow is remarkable for his time because whereas all other characters in the novella are either cruel or indifferent to the situation of the Africans, Marlow is sometimes disturbed by what is witnessing. Conrad uses this to show the reader the effects of European Imperialism on Africa and in particular in the Belgian Congo.

A good example of this is when Marlow first arrives at the Outer Station and witnesses the Africans at work. He says, "Black shapes crouched, lay, sat between the trees leaning against the trunks, clinging to the earth, half coming out, half effaced within the dim light, in all the attitudes of pain, abandonment, and despair. Another mine on the cliff went off, followed by a slight shudder of the soil under my feet. The work was going on. The work! And this was the place where some of the helpers had withdrawn to die." This is just one instance where Marlow seems to be able to 'see' the black men as humans. Conrad uses the character of Marlow to present the Africans in a more senstive manner however, by today's standards many of Marlow's observations seem very ignorant and therefore appear racist to us.

This isn't an either/or question. Yes, you could say that Conrad's work is racist, but if you dismissed it for that reason, you'd be dismissing it too fast, because yes, there is much more to it.

Conrad's work is racist in how it portrays Africans, and in how it treats Africa as a site of transforming mystery. The darkness of the jungle fuses with the darkness of native skins and the darkness of the human heart. Conrad uses Africans not as characters most of the time, but as symbols of dark passion and savagery.

However, the book is more than simply racist, because he also critiques the system that produces this division, and shows what happens when men live with such attitudes. He also produces deeply poetic visions of madness/passion that remain useful even when we adjust for the racism.

Is Heart of Darkness a racist story?

The Heart of Darkness is held by some to be a racist story, but in my opinion it is not.  There is a famous essay by Chinua Achebe, which holds that the story is racist, and I have provided a link to that essay for you.  Whether or not the story is racist is a judgement you will want to make for yourself.  Quite often, a literary text will contain evidence to support different points of view, and each of us brings a different perspective to a text, as well.

From my perspective, if you read the story carefully, you will see that it is the colonial British who are painted as incompetent, ineffective, and inhumane.  Their machinery is rotting, they have no idea how to live in this land, and they manage the natives with casual cruelty. They are portrayed as being rigid and maladaptive. In short, what is shown is how foolish and uncivilized the white man is.  Most of the negative portrayals of the natives show the white man as the cause of the problem.

If you are expected to write an essay or even a brief response to your question, you will want to go through the story and ask yourself whether or not the scenes are providing a negative portrait of the natives or a negative portrait of the British.  Use the text to support your opinion.