The pion electromagnetic form factor is calculated within the QCD light-cone sum rule method and using a renormalon model for the higher twist distribution amplitudes (DAs). The theoretical predictions are compared with the experimental data and constraints on the pion leading and twist-4 DAs are extracted. An upper bound on the twist-4 contribution to the form factor and estimates of effects due to higher conformal spins in the pion twist-4 DAs are obtained.