Conceivably. It could be slander, and if it affected your employment, you would have a definite injury.
Is it a former employer or someone in your life? Many bosses are not unfamiliar with drama in people's personal lives, but it is something you'll need to address because a boss can easily decide "this is too much crap to put up with".
The first steps are asking your boss for a couple of minutes and explaining the situation, determining how they feel about it; then dealing with the person who may be sending the messages. From there, it probably goes to HR, and that's a whole mess of trouble, and in extremis, I'd imagine you could find a lawyer to write a cease and desist letter (don't be surprised if it's something like a couple hundred bucks), or possibly get a restraining order.
Not enough info to help you out much more than that, though.