A general analytic expression for bootstrap current driven by fusionborn alpja particles is obtained in a deutrium-tritium tokamak plasma using a kinetic variational theory. A self-adjoint form of linearized coulomb collision operator, which includes both energy and pitch angle collisions, has been used. 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 (ITERCDA) parameters. The result agrees well with results obtained using another technique [Hsu et al. Phys. Fluids B4, 4023(1992)].