We examine the possibility for testing the weak parity non-conserving (pnc) interaction in pion-nucleon scattering at low energies. We start out analysis by assuming the existence of a pnc πNN coupling which conserves time reversal invariance and has the isospin selection rule ΔI = 1, and the existence of fixed- t dispersion relations obeyed by the pnc invariant amplitudes. By using the nonrelativistic expansion, we then derive dispersion relations for the partial-wave amplitudes. We calculate parity-odd observables in π −p → π −p and in π −p → π 0n, e.g., the up-down asymmetry α in the total cross section for a polarized target and the longitudinal polarization P of the recoil nucleon. In the conventional Cabibbo model for the weak interaction P and α are found to be of order 10 −7 to 10 −8. We have also examined the t-channel pnc ϱ-exchange process which has the isospin selection rule ΔI = 0, 2 and found it to contribute dominantly to P in the charge-exchange channel π −p → π 0n.