  Intrinsic variations of the projected density profiles of clusters of
galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We
present a semi-analytical model to account for this effect, based on a
combination of variations in halo concentration, ellipticity and orientation,
and the presence of correlated haloes. We calibrate the parameters of our model
at the 10 per cent level to match the empirical cosmic variance of cluster
profiles at M_200m=10^14...10^15 h^-1 M_sol, z=0.25...0.5 in a cosmological
simulation. We show that weak lensing measurements of clusters significantly
underestimate mass uncertainties if intrinsic profile variations are ignored,
and that our model can be used to provide correct mass likelihoods. Effects on
the achievable accuracy of weak lensing cluster mass measurements are
particularly strong for the most massive clusters and deep observations (with
~20 per cent uncertainty from cosmic variance alone at M_200m=10^15 h^-1 M_sol
and z=0.25), but significant also under typical ground-based conditions. We
show that neglecting intrinsic profile variations leads to biases in the
mass-observable relation constrained with weak lensing, both for intrinsic
scatter and overall scale (the latter at the 15 per cent level). These biases
are in excess of the statistical errors of upcoming surveys and can be avoided
if the cosmic variance of cluster profiles is accounted for.
