No; having tattoos is not a protected class under US employment law. Therefore, if that is the sole reason that someone chose not to hire you, then it would be a permissible decision. read more
It is within their rights not to hire a person that has visible tattoos. You will also see job ads that state "no tattoos." Companies are allowed to require a particular 'look' for their employees within reason and as Cliff points out, tattooed people are not a protected class. So no, it is not illegal to deny you employment because of your tattoos. read more
Most employment relationships are what is known as "at will". This means that you can work for an employer, or not, your choice. In turn, the employer can hire or fire someone for any reason or no reason whatsoever. read more