Radio Free Asia Act of 1993 - Amends the Board for International Broadcasting Act of 1973 to authorize the Board for International Broadcasting to designate one organization constituted on the model of Radio Free Europe/Radio Liberty (RFE/RL), Incorporated, to carry out radio broadcasting to China, Tibet, Burma (a.k.a. Myanmar), Cambodia, Laos, North Korea, and Vietnam. Designates such broadcasts as Radio Free China. Increases the number of Board members. Limits terms of Board members who are presidential appointees to three years. Sets forth additional provisions concerning membership terms.