Office for Access to Justice Establishment Act of 2020 This bill establishes the Office for Access to Justice within the Department of Justice (DOJ) to advise on matters relating to justice for low-income and other people in the criminal and civil justice systems. Additionally, DOJ must establish a Legal Aid Interagency Roundtable to raise the awareness of executive branch agencies of the ways in which civil legal aid and indigent defense can help advance federal objectives, including those related to employment, family stability, housing, consumer protection, health services, and public safety.