I recommend scheduling a visit with your primary care doctor
to discuss this issue. Psoriasis, as you probably know, is an inflammatory condition which usually affects the skin by producing red, scaly, itchy lesions which can range from very mild to quite severe. It can also have other symptoms, such as arthritis
Psoriasis definitely is associated with some genetic factors. Around 40% of individuals with psoriasis have a close family member who also has the condition, which underscores this point. At the same time, that means that 60% of people with psoriasis don't have a family history, so just having a family member with psoriasis doesn't mean you are destined to develop the condition yourself.
For people who do have psoriasis, any damage or trauma to the skin can be a site for a flare up of the condition. For example, people with psoriasis may develop skin lesions at the site of a new tattoo. That being said, there is no evidence, if you do not have psoriasis, that getting a tattoo will trigger the onset of the condition.
Again, it is worth scheduling a visit with your primary care doctor or dermatologist to discuss this issue. They'll be able to examine your skin for any evidence of the condition and help you decide whether getting a tattoo is worth the risk.