  We study the dependence of surface mass density profiles, which can be
directly measured by weak gravitational lensing, on the orientation of haloes
with respect to the line-of-sight direction, using a suite of $N$-body
simulations. We find that, when major axes of haloes are aligned with the
line-of-sight direction, surface mass density profiles have higher amplitudes
than those averaged over all halo orientations, over all scales from $0.1$ to
$100\,\mathrm{Mpc}/h$ we studied. While the orientation dependence at small
scales is ascribed to the halo triaxiality, our results indicate even stronger
orientation dependence in the so-called two-halo regime, up to
$100\,\mathrm{Mpc}/h$. The orientation dependence for the two-halo term is well
approximated by a multiplicative shift of the amplitude and therefore a shift
in the halo bias parameter value. The halo bias from the two-halo term can be
overestimated or underestimated by up to $\sim 30 \%$ depending on the viewing
angle, which translates into the bias in estimated halo masses by up to a
factor of two from halo bias measurements. The orientation dependence at large
scales originates from the anisotropic halo-matter correlation function, which
has an elliptical shape with the axis ratio of $\sim 0.55$ up to $100\,
\mathrm{Mpc}/h$. We discuss potential impacts of halo orientation bias on other
observables such as optically selected cluster samples and a clustering
analysis of large-scale structure tracers such as quasars.
