That is a great question.
You might think of the voice as Maya Angelou speaking for a larger group, like an ambassador or diplomat speaking for a nation, or a minister speaking for a church. The thoughts expressed represent something larger than just the speaker--more than just Angelou--but are something that the speaker sees as true and important for the group.
To put it another way, look at this line late in the poem: "I am the dream and the hope of the slave."
That's telling us that this voice is meant to represent a strong, free, proud African American, someone who lives and embodies what slaves hoped and dreamed might someday be true. This is Maya Angelou, who gives a proud voice to the African American experience but it is also larger than just her. This is the voice of the free, idealized, black American.