No, Penguins do not live in igloos. The people who traditionally made igloos are the Inuit, who live in far Greenland and north of North America, where there are no penguins. There are also no people native to Antarctica, where some penguins live but not all.
Igloos are made by slicing thick snow into bricks and then stacking them in a specific manner. Since penguins don’t have knives or hands or saws, a penguin would have a hard time building an igloo, even if it was intellectually capable of it.