There is some debate over the risks involved when getting a tattoo whilst pregnant. After some research, it seems like it is very unlikely any respectable and caring tattoo artist will be willing to tattoo you if you are carrying an unborn child.
Several artists commented on the possible risks, including premature labour, shock, infection and the simple fact not enough is known on the strain to the body.
When you get a tattoo, your body reacts to the pain and shock by pumping adrenaline round your body. Your heart rate increases, your skin sweats and your body fights the invasive procedure of getting a tattoo. Whilst carrying a baby, this adrenaline and shock can induce labour prematurely, thus it is not adviseable to even think of getting a tattoo whilst pregnant.
Further to that, tattoos can be prone to infection if not cared for properly. Artists provide general advice on looking after your tattoo but it is not fullproof and your general hygiene can cause an infection. If your body is carrying a child, it is already under tremedous strain and fighting an infection at the same time may be too much. Further to that, the infection may spread fas and onto your baby.
Little factual research is available on the subject but common knowledge would suggest getting a tattoo whilst pregnant is not a good idea.