Can you have an alcoholic drink while taking topiramate?

Not recommended. With any med that affects mood and or memory alcohol would not be recommended. Not sure why you are on it, however it is used for persons with alcohol problems, it can decrease cravings and make alcohol less rewarding.
Ask your doctor. This depends on why you are taking it and will depend on your physician's guidance. Your diagnosis like seizures for which it is used, or migraine may also guide your physician's advice.