I have psoriasis and I want a tattoo, can I do that?

Yes. But as you know, damage to the epidermis can trigger psoriatic reactions in those locations. Your dermatologist might better be able to answer this but it should be okay for you to do it although there are alternative reasons not to do this, just one of which is the psoriasis.
Carefully. It is possible for the tattooing to cause a localized flare of the psoriasis in the area. Psoriasis can develop at sites of trauma.