We constrain a stochastic background of primordial magnetic field (PMF) by its contribution to the angular power spectrum of cosmic microwave background anisotropies. We parametrize such stochastic background by a power-law spectrum with index n_B and by its Gaussian smoothed amplitude B_λ on a comoving length λ. We give an approximation for the spectra of the relevant correlators of the energy-momentum of the stochastic background of PMF for any n_B. By using the WMAP 7 year data in

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... with ACBAR, BICEP and QUAD we obtain the constraint B_1 Mpc < 5.0 nG at 95 level for a stochastic background of non-helical PMF. We discuss the relative importance of the scalar and vector contribution to CMB anisotropies in obtaining these constraints. We then forecast Planck capabilities in constraining B_1 Mpc.