We present a model of ant traffic considering individual ants as self-propelled particles undergoing single file motion on a one-dimensional trail. Recent experiments on unidirectional ant traffic in well-formed natural trails showed that the collective velocity of ants remains approximately unchanged, leading to absence of jamming even at very high densities [ John et. al., Phys. Rev. Lett. 102, 108001 (2009) ]. Assuming a feedback control mechanism of self-propulsion force generated by each ant using information about the distance from the ant in front, our model captures all the main features observed in the experiment. The distance headway distribution shows a maximum corresponding to separations within clusters. The position of this maximum remains independent of average number density. We find a non-equilibrium first order transition, with the formation of an infinite cluster at a threshold density where all the ants in the system suddenly become part of a single cluster.