We present a family of charged rotating wormhole solutions to the Einstein-Maxwell equations, supported by anisotropic matter fields. We first revisit the charged static cases and analyze the conditions for the solution to represent a wormhole geometry. The rotating geometry is obtained by applying and modifying the Newman-Janis algorithm to the static geometry. We show the solutions to Maxwell equations in detail. We believe that our wormhole geometry offers a geometric realization corresponding to the concept of `charge without charge'.

28 pages, 3 figures, Error fixed