If the tattoo is new and still healing itching is totally normal. Te best thing to do is just wash it if it itches and apply aquaphor cream. If your tattoo is older it may be a bug bite, a rash or eczema causing the itch.
Assuming this is a new tattoo, the itching is caused by the skin healing after having all the tiny holes poked into it as well as the skin adjusting to the new ink underneath it.
Your tattoo will usually be itchy as it is going through the healing process. You may experience itching as it begins to heal days after you get your tattoo. The itching should stop as it is healed.
i have had many tattoos, ice or very cold water always works for me once it gets to the itchy stage, as well as keeping it moisturized by applying a thin layer of A&D or Aquaphor everyday.