Do I have a claim if I couldn’t get promotion because of my tattoo?

I know that you feel discriminated against but the fact of the matter is that employees do not have to be treated equally or even fairly. It is compleely legal to treat one employee differently from others as long as such treatment does not violate company policy or a union/employment contract. Also, if differing treatment is the result of actionable discrimination it is illegal. In other words, there can be no discrimination in employment based on such factors as: race, religion, gender, age, disability, sexual orientation, national origin. So for example, if you were denied the promotion because you were Hispanic (i.e. due to your status in a legally protected class) that would be against the law. This means that an employer has complete discretionis setting the terms and conditions of the workplace. In other words, unless you are a member of a legally protected class, discrimination is perfectly permissible (and having a tattoo does not put you in such a class).

Specifically, if an employer doesn't an employee's appearance or believes that a certain appearance does not put forward the image that it wants, it can deny an employee a promotion (or even hiring that employee). Agree with it or not, tattoos and other body art draws certain images or connotations that may not comport with corporate culture or be acceptable to the customers or clients the company services. Bottom line, a company has the right to put forth the image that it wants.