The importance of the initial current rise phase of a toroidal, magnetically confined plasma to the fusion ignition of a deuterium-tritium mixture at high magnetic field and current is pointed out. Numerical results from the simulation of a free boundary plasma, using the axisymmetric transport and MHD evolution code TSC, extend and verify the analytic and experimental results. The current ramp can drive a large amount of Ohmic heating at high central temperatures and can contribute significantly to reaching ignition in high field machines. Simultaneous control of the rate of current rise, the plasma shape and position, and the plasma density allows D-T ignition to be attained with stable, monotonically decreasing toroidal current density profiles and with magnetic field line parameters q(ψ) that do not lead to large sawtooth oscillations, when the plasma current diffuses under a collisional (neoclassical) resistivity alone. The results apply to existing low q plasmas and suggest the possibility of control of the electron temperature in the central and outer regions of the plasma to enhance both current density control and ignition