Having tattoos does not stop you from becoming an egg donor.
Generally, the clinics have a policy which states that you cannot have had the tattoo(s) in the last 12 months.
This is to ensure that you haven't picked up any nasties from the tattooist that take some time to show in your blood such as HIV etc.
Good on you for wanting to become a donor. I am sure that you will make a couple very happy.