The prospects for the measurement of the tensor structure of the vertex between a standard model Higgs boson and two weak gauge bosons using the distribution of the azimuthal angles between the two tagging jets in the weak boson fusion channel are studied in a Monte Carlo analysis using the fast simulation of the ATLAS detector. The decay channels H→τ+τ−→ll+4ν, H→τ+τ−→lh+3ν at mH=120GeV and H→W+W−→llνν at mH=160GeV are used in the analysis. For a standard model Higgs boson it is found that purely anomalous couplings are expected to be excluded at a confidence level corresponding to 2\,σ or more at mH=120GeV and more than 5\,σ at mH=160GeV from 30fb−1 of data. With a value of 1 roughly reproducing the standard model cross section for a purely anomalous coupling, the standard deviation in a measurement of a contribution of a CP even anomalous coupling in addition to the standard model coupling is estimated to be 0.20 at mH=120GeV and 0.08 at mH=160GeV