B) Red blood cells carry oxygen to muscle tissue(erythrocytes) Which Cells Carry Oxygen. For the best answers, search on this site https://shorturl.im/av1SC Red Blood Cells. Lung cells and Artery cells are responsible for structural support. They do not carry oxygen. Nerve cells are responsible in carrying electrical signaling from the nervous system. They do not carry oxygen. Red blood cells contain hemoglobin which is able to bind to oxygen molecules. The red blood cells take up oxygen in the lungs and move through the capillary blood vessels to tissue in the body, including muscle tissue, all along the way releasing oxygen to surrounding tissue that is being taken up and used by cells for energy production.