A charge and current deposition method is presented for electromagnetic particle-in-cell simulations in 3D cylindrical coordinates using Yee's grid. The method is a direct extension of Villasenor and Buneman's current deposition method from Cartesian to 3D cylindrical coordinates, through computing the volumes swept by cylindrical sector charges over the current density surfaces. Along with Verboncoeur's correct volume terms for cylindrical coordinates, the method satisfies the continuity equation rigorously and eliminates edge errors.