No—pit bulls are effectively banned in Japan. They are classified as "dangerous dogs" (特定犬) under the Act on the Protection and Management of Animals, alongside Tosa Inu, Akita Inu, and mixes.
Many prefectures (Tokyo, Kanagawa, Osaka, etc.) have outright bans on ownership, breeding, and import of pit bulls. Violations → fines, imprisonment, or euthanasia of the dog.
Bottom line: Do not attempt to bring or acquire a pit bull in Japan. Choose a non-restricted breed.