The absorption of pi^+ on ^3He in the $Delta$-region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $pi N to Delta$ vertex and a $NDelta - NN$ transition t-matrix which are calculated from a phenomenological model for NN and pi d reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ^2H and ^3He lie too high in energy in relation to the data. The effect of the final state three-nucleon interaction turns out to be too small for changing the magnitude and shifting the peak position of the total absorption cross section for ^3He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the $Delta$-parameters, automatically leads to the correct peak position in ^3He.
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