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The scintillation index of a Gaussian Schell-model beam with twist phase (i.e., twisted GSM beam) in weak turbulent atmosphere is formulated with the help of a tensor method. Variations of the scintillation index of a twisted GSM beam on propagation in turbulent atmosphere are studied in detail. It is interesting to find that the scintillation index of a twisted GSM beam can be smaller than that without twist phase in weak turbulent atmosphere. Thus, modulation of the twist phase of a partially coherent beam provides a new way to reduce turbulence-induced scintillation.