Can rejection of an organ cause severe itching, my husband had his liver transplanted?

Yes. Rejection itself does not cause itching. If the bilirubin is up during an episode of rejection it can irritate the skin and cause itching.
Pehaps. Rejection can cause an organ to dysfunction and result in the accumulation of certain toxins or minerals that could lead to itching. Also, itching can result form the use of other medications. You should discuss this with your transplant doctors that are managing your care.