It Depends
What is it?
Xanthan gum is a substance used in many different foods as well as industrial products because it can thicken their consistency. It has amazing emulsifying properties, whereby it can help different ingredients mix together. It's often used in ice cream, yogurt, jellies, salad dressings, and can be used to thicken drilling mud in the oil industry. It is generally considered safe to consume in small quantities.
Is it vegan?
The process by which xanthan gum is produced may be helpful in answering this question. It's a polysaccharide produced when a specific kind of bacteria ferments corn sugar. So, the fact that it's derived from bacterial fermentation should mean it's vegan-friendly, right? Not quite. Some xanthan gum can be made using chicken lysozymes - which, of course, is not vegan. It can also sometimes be derived from milk, so check the package for an allergy warning. If you really want to verify whether or not animal products have been used in a specific brand of xanthan gum or product containing xanthan gum, contact the manufacturer. Also, look for products that are specifically marked as being vegan-friendly.
Also see: Is Xanthan Gum Bad For You?