The NICOTINE in cigarettes causes narrowing of the blood vessels in the outermost layers of your skin. This impairs blood flow to your skin. With less blood flow, your skin doesn't get as much oxygen and important nutrients, such as vitamin A.
It is also associated with increased wrinkling and skin damage on other parts of your body, including your inner arms.
http://www.mayoclinic.org/healthy-living/quit-smoking/expert-answers/smoking/faq-20058153