Nicotine and carbon monoxide in tobacco reduces the amount of oxygen in the blood, as well as damage the blood vessel walls which not only help strokes to start from oxygen deprivation directly but can cause clots more easily. On top of this, cigarette smoke also greatly increases the risk of coronary heart disease, which when acting with other pre-existing stroke risk factors greatly increases the chances of having one. Smoking even makes those other factors more easily able to crop up, as smoking increases blood pressure (a risk factor), decreases your tolerance to healthy amounts of exercise (another risk factor) and increases the tendency for blood to clot (see a pattern, here?) Most importantly, as strokes are more likely for people over 60, smoking can dramatically increase the odds of having an early-life stroke for people under the age of 50 (you can take a guess as to what it does to your chances over 50).
For more information on strokes, you can visit strokeinfo.org.