We present an experimental route to engineer the exciton energies of single quantum dots in nanowires. By integrating the nanowires onto a piezoelectric crystal, we controllably apply strain fields to the nanowire quantum dots. Consequently, the exciton energy of a single quantum dot in the nanowire is shifted by several meVs without degrading its optical intensity and single-photon purity. Second-order autocorrelation measurements are performed at different strain fields on the same nanowire quantum dot. The suppressed multi-photon events at zero time delay clearly verify that the quantum nature of single-photon emission is well preserved under external strain fields. The work presented here could facilitate on-chip optical quantum information processing with the nanowire based single photon emitters.