If you want a tattoo, go for it! There are no rules on whether or not a person can have body art in the engineering profession (at least for the USA).
However, some companies prefer that if you do have body art, that it can be easily, or at least mostly, covered by business and/or business casual clothing. I would suggest reaching out to professionals in the engineering disciplines you're interested in and see what is common for their industry.
While I personally do not believe that it should matter (personal belief, not representative of Engineer Girl or Lockheed Martin), some companies do have rules around body art. Just be mindful of that if you plan on getting a tattoo in the future.