Any trauma to the skin in a patient with psoriasis can cause the typical plaques of psoriasis to develop, a phenomenon known as the Koebner response. So can getting a tattoo cause the Koebner response? The answer is an unequivocal: yes. In fact, Dr. Koebner himself reported the development of psoriasis in a tattoo way back in 1872.
That being said, there are many people with psoriasis who can get tattoos without any problems. First decide: Is the tattoo really necessary? Then speak with your doctor about the risks involved. If a plaque of psoriasis develops due to a tattoo, it can likely be treated. Also, psoriasis doesn't always immediately develop right after getting a tattoo -- it may show up years later in the same spot as the tattoo.
source: Horner KL, Chien AJ, Edenholm M, Hornung RL. Winnie the Pooh and psoriasis too: an isomorphic response of guttate psoriasis in a tattoo. Pediatr Dermatol 2007;24:E70-2