Do red blood cells have nucleus?
No, mature red blood cells lack a nucleus.
When red blood cells (erythrocytes) are produced in the bone marrow, they initially do contain a nucleus. In maturation the cell will extrude its nucleus, a process called enucleation. When the red blood cells enter circulation, they don't have a nucleus.
The lack of a nucleus is an adaptation of the cell to be better equipped for its task. The lack of a nucleus allows it to carry more oxygen. The cell is also more flexible, improving its ability to travel through capillaries that are about half the size of the cell itself.