  We show how transverse beam polarization at $e^+e^-$ colliders can provide a
novel means to search for CP violation by observing the distribution of a
single final-state particle without measuring its spin. We suggest an azimuthal
asymmetry which singles out interference terms between standard model
contribution and new-physics scalar or tensor effective interactions in the
limit in which the electron mass is neglected. Such terms are inaccessible with
unpolarized or longitudinally polarized beams. The asymmetry is sensitive to CP
violation when the transverse polarizations of the electron and positron are in
opposite senses. The sensitivity of planned future linear colliders to
new-physics CP violation in $e^+e^- \to t \bar{t}$ is estimated in a
model-independent parametrization. It would be possible to put a bound of $\sim
7$ TeV on the new-physics scale $\Lambda$ at the 90% C.L. for $\sqrt{s}=500$
GeV and $\int dt {\cal L}=500 {\rm fb}^{-1}$, with transverse polarizations of
80% and 60% for the electron and positron beams, respectively.
