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• Exact cylindrically symmetric solutions in the context of Rastall theory of gravity. • The modified field equations in the presence of charge. • To recover the well-known Levi-Civitas static cylindrically symmetric solution in the framework of Rastall gravity. • The graphical behavior of energy density and pressure component along with the discussion of energy conditions. In this paper, we explore some exact cylindrically symmetric solutions in the context of Rastall theory of gravity. For this purpose, we consider the general form of a metric in the cylindrical Weyl coordinates. The modified field equations are developed in the presence of charge. In particular, we try to recover the well-known Levi–Civita's static cylindrically symmetric solution in the framework of Rastall gravity. The graphical behavior of energy density and pressure component is presented along with the discussion of energy conditions. Finally, the solutions in the context of general relativity are discussed. It is concluded that Levi–Civita's static cylindrically symmetric charged solutions do exist in Rastall theory of gravity. [ABSTRACT FROM AUTHOR]