He fulfilled his military service in Sivas as a military judge. Between 1988 and 2000, he served as a member of the Board of Directors of the Afyonkarahisar Bar Association, and following the Extraordinary General Assembly held in 2001, he was elected President of the Afyonkarahisar Bar Association.
While serving as Bar President, after the constitutional amendment in 2010, he was nominated as one of three candidates selected by bar association presidents. Following the vote held at the General Assembly of the Turkish Grand National Assembly on October 13, 2010, he was appointed as a member of the Constitutional Court.
During his tenure at the Constitutional Court, he was elected President of the Court of Jurisdictional Disputes. He retired from these positions on January 31, 2022, due to the age limit.
Celal Mümtaz Akıncı is married and has four children.
