Could I sue someone who claimed me as their dependent on their taxes?

You can sue them. The issue is was damages you can collect. Did it cause you to spend money for to properly claim your exemption?

You can sue anybody for darn near anything, but I do not understand why you would sue either the party claiming you or the tax preparer. It appears that there are additional facts which are missing, you are advised to seek a limited consultation with an attorney to explain all of the facts and circumstances and receive a reasoned opinion about your potential options.