Hi there!
Nurses absolutely can have tattoos! There may be certain rules private employers have relating to tattoos and visibility of them so we would advise you be conscious of that. Across our nursing and healthcare courses we have had many students who have had tattoos. Employers attitudes are slowly changing regarding tattoos and they are generally much more accepted than they were in the past. I would say the two things to consider would be: Will it be visible? Is it possible someone may reasonably find the tattoo offensive?
Best of luck with your course and wishing you luck in your career!