  In the presence of spin-orbit coupling, electron scattering off impurities
depends on both spin and orbital angular momentum of electrons -- spin-orbit
scattering. Although some transport properties are subject to spin-orbit
scattering, experimental techniques directly accessible to this effect are
limited. Here we show that a signature of spin-orbit scattering manifests
itself in quasiparticle interference (QPI) imaged by spectroscopic-imaging
scanning tunneling microscopy. The experimental data of a polar semiconductor
BiTeI are well reproduced by numerical simulations with the $T$-matrix
formalism that include not only scalar scattering normally adopted but also
spin-orbit scattering stronger than scalar scattering. To accelerate the
simulations, we extend the standard efficient method of QPI calculation for
momentum-independent scattering to be applicable even for spin-orbit
scattering. We further identify a selection rule that makes spin-orbit
scattering visible in the QPI pattern. These results demonstrate that
spin-orbit scattering can exert predominant influence on QPI patterns and thus
suggest that QPI measurement is available to detect spin-orbit scattering.
