We present an iterative approach which uses the Schwinger variational principle to solve the Lippmann-Schwinger equation for electron-molecule scattering. This method combines the use of discrete basis functions to describe the effects of the noncentral molecular potential with an iterative procedure which provides systematic convergence of the scattering solutions. Results for electron-H2 scattering in the static-exchange approximation show that the method converges rapidly and gives very accurate results.