The Red-tailed Hawk (Buteo jamaicensis) is a bird of prey, one of three species colloquially known in the US as the chickenhawk, though it rarely preys on chickens. Females are on average about 25 per cent heavier than males.
The Red-tailed Hawk ia also significant in Native American culture. The feathers are used in religious ceremonies and considered sacred by some tribes.
This imagery connects to the idea of Shug, in Celie's mind, as larger than life and sacred.