The analysing power A\sbN of inclusively produced charged pions is measured using 13.3 and 18.5 GeV/c polarized protons from the Brookhaven AGS. The measurement was performed at the Multiparticle Spectrometer in early 1986, in conjunction with a measurement of inclusively produced Λ particles. There are two possible theoretical explanations for the data. A baryon exchange model is discussed in light of the previous measurements of the pion analysing power. This model is dependent on the scanty backward πp elastic data that is available at lower energies. A more modern quark recombination model which uses SU(6) symmetry and the idea that the spin of the quarks is preserved in the scattering and recombination process is used to make specific predictions concerning the analysing power of inclusively produced particles. The quark model predicts that A\sbN should be positive for π\sp+ and negative for π\sp− in the beam fragmentation region. The data analysis consists of pattern recognition and track reconstruction of the tracks in the spectrometer, and identification of the pions. The background consists of particles that did not originate in the target, and particles which may have passed through the edges of drift chamber frames. Minimal cuts are applied to the data, requiring that the pions come from the target and pass through the drift chamber active areas. The acceptance of the apparatus was verified by Monte Carlo calculation. The measured vertical component of the beam polarization P\sbN was 0.379 ± 0.020 at 18.5 GeV/c. At 13.3 GeV/c, P\sbN was measured to be 0.5900 ± 0.0130. The analysing power for π\sp− over the range of 0.1 ≤ X\sbF ≤ 0.7 was found to be almost negligible, with a value of 0.0037 ± 0.0036 at 13 GeV/c when calculated for all transverse momenta. A\sbN for π\sp− is observed to be negative in the highest X\sbF-P\sbT bin measured. The π\sp+ analysing power is found to be positive, increasing approximately linearly with increasing X\sbF, and is observed to have a flat dependence upon P\sbT, with a value of 0.047 ± 0.0034 when averaged over all P\sbT and X\sbF. Our measurement is found to be in qualitative agreement with the predictions of the quark recombination model.