Is it ok to drank 8 0z of tart cherry juice with 325 mg of aspirin?

Yes. As long as it doesn't cause you to develop symptoms of acid reflux (indigestion, heartburn) there will be no problem. Some worry about aspirin's potential to cause erosion and inflammation of the stomach lining (gastritis) and subsequent ulcer but most do not have a problem with this and if it occurs, pain in your upper abdomen and nausea will let you know.