Abelian gauge theory in d\neq 4 spacetime dimensions is an example of a scale invariant theory which does not possess conformal symmetry -- the special conformal transformation(SCT) explicitly breaks the gauge invariance of the theory. In this work, we construct a non-local gauge-invariant extension of the SCT, which is compatible with the BRST formalism and defines a new symmetry of the physical Hilbert space of the Maxwell theory for any dimension d\geqslant 3. We prove the invariance of the Maxwell theory in d\geqslant 3 by explicitly showing that the gauge-invariant two-point correlation functions, the action, and the classical equation of motion are unchanged under such a transformation. Show Partial Abstract