Do carotid stents cause strokes?

Possible. It is possible to develop a stroke during carotid stent placement (~ 4% in optimal patients). However the carotid stent is effective at preventing further strokes and that is why they are placed. At this point carotid stents are reserved for patients who are at high risk for open carotid endarterectomy (surgery).
Yes. The gold standard for carotid disease is a carotid endarterectomy. The stroke rates for this procedure in properly trained individuals is very low. This is generally lower than the stroke rate for carotid stenting. The real problem with the carotid stent is the recurrence rates long term and no one knows the answer to that at this time.
It is a risk. Stroke is a known risk of carotid stenting. It is also a risk of the surgical option: endarterectomy. Your, or your family member's risk of stroke is best explained by your physician. But do recognize that carotid stenosis - the need for the stent/surgery - puts one at risk of transient ischemic attack (tia), stroke or even death.
Risk. One of the risks of carotid stent placement is a stroke. Check with the physician who is doing the procedure to see his stroke rate. Make sure protection device is used to increase safety. Experienced doc should have rate less than 5%.