When I do a Google search, most of the results are about whether or not people can get HIV / AIDS from getting a tattoo through dirt needles. I am, however, curious whether or not it is possible to get a tattoo if you have AIDS.
Quoting wikipedia's entry on tattoos:
Tattooing involves the placement of pigment into the skin's dermis, the layer of dermal tissue underlying the epidermis. After initial injection, pigment is dispersed throughout a homogenized damaged layer down through the epidermis and upper dermis, in both of which the presence of foreign material activates the immune system's phagocytes to engulf the pigment particles.
If your immune system is not working properly, I can imagine that the phagocytes might never respond to the tattoo ink and that the pigment might not ever enter the fibroblasts?