Charmonium production in pp collisions with ALICE at the LHC

We report on forward-rapidity charmonium production in pp collisions at a center of mass energy $\sqrt{s} = 13$ TeV, as measured by ALICE at the LHC. Differential cross sections for both J/$\psi$ and $\psi$(2S) are presented as a function of the charmonium transverse momentum and rapidity. Results are compared to similar measurements performed by LHCb, to lower energy measurements and to state of the art model calculations.