The propagation of ion acoustic (IA) solitary waves is investigated in a magnetized electron‐positron‐ion (EPI) plasma with Tsalli distributed electrons and Maxwellian positrons. A non‐linear Korteweg–de Vries (KdV)‐type equation is derived for the potential by using the reductive perturbation method (RPM), and its solitary wave solution is analysed. For a given set of plasma parameters, the present model supports only compressive IA solitary structures. It is found that the variation of various relevant plasma parameters, like the nonextensive parameter q, temperature ratio σ, direction cosine l_z, the positron concentration γ and the magnetic field strength significantly alter the characteristic properties of IA solitary waves.