A general analytic expression for bootstrap current driven by fusion-born alpha particles is obtained in a deutrium-tritium tokamak plasma using a kinetic variation theory. A self-adjoint form of linearized Coulomb scattering operator has been used, which includes both energy and pitch angle collisions. The formula is applied to predict alpha-driven bootstrap current in a reactor condition similar to that of the International Thermonuclear Experimental Reactor Conceptual Design (ITER CDA) parameters [ITER Documentation Series, Number 18 (International Atomic Energy Agency, Vienna, 1991)]. The result agrees well with results obtained using another technique [Hsu et al., Phys. Fluids B 4, 4023 (1992)]. (C) 1996 American Institute of Physics.