If the person borrowing your car is only ticketed for driving under the influence (DUI) and was not in an accident while intoxicated than normally this would not affect your car insurance rates. The person that was using your vehicle should have received the citation in their name so that the DUI will go on their record and not cause you any issues.

However if the person was in an accident with your car during this time than the resulting claims would go on your claims record and thus could affect your insurance premiums. Auto insurance typically follows a car first and driver second meaning that if your friend was driving drunk in your car then it would be your insurance policy that would be gone to primarily and the friend's insurance would be secondary or excess if your limits were exceeded.

Keep in mind though when loaning out your car to others that as owner of the car you have vicarious liability for those that you allow to drive it. This mean if all insurance limits were exceeded then in most states the driver and you may be held liable for any damages he or she caused while operating your vehicle. If the person was under the influence of alcohol or drugs and severely injured someone in an accident than your personal finances and assets could be at risk.