We propose a simple method to calculate the pion form factor at not very large momentum transfers, which combines the technique of the QCD sum rules with the description of the pion in terms of the set of wave functions of increasing twist. This approach allows one to calculate the soft (end point) contribution to the form factor in a largely model-independent way. Our results confirm existing expectations that the soft contribution remains important at least up to the momentum transfers of order 10 GeV$^2$, and suggest that it comes from the region of relatively small transverse separations of order 1 GeV$^{-1}$.