  Intrinsic alignment (IA) of source galaxies represents an important
contaminant for upcoming cosmic shear surveys. In particular, it is expected on
general grounds that IA contains a B-mode while the weak lensing signal does
not. Thus, a detection of B-modes offers the possibility to study directly the
IA signal of the sources. Galaxy clusters exhibit strong IA and are therefore a
natural candidate to look for a B-mode signal. We forecast the signal-to-noise
ratio (SNR) for B-modes from IA of galaxy clusters in the Vera C. Rubin
Observatory Legacy Survey of Space and Time (LSST). We use a perturbative model
for the IA multipoles based on the Effective Field Theory of Intrinsic
Alignments (EFT of IA), which has recently been validated against N-body
simulations. We forecast SNR $\approx 12$ and find that this detectability is
not significantly impacted by different analysis choices. Lastly, we also apply
our forecast to clusters in the redMaPPer SDSS and DESY1 samples. We find SNR
$\approx 5$ and SNR $\approx 3$, respectively, suggesting a detection is within
reach, provided accurate redshift information is available.
