  We show that in free surface flows, a uniform, streamwise current over
small-amplitude wavy bottom topography generates cross-stream drift velocity.
This drift mechanism, referred to as the current-bathymetry interaction induced
drift (CBIID), is specifically understood in the context of a simplified
nearshore environment consisting of a uniform alongshore current, onshore
propagating surface waves, and monochromatic wavy bottom making an oblique
angle with the shoreline. CBIID is found to originate from the steady,
non-homogeneous solution of the governing system of equations. Similar to
Stokes drift induced by surface waves, CBIID also generates a compensating
Eulerian return flow to satisfy the no-flux lateral boundaries, e.g. the
shoreline. CBIID increases with an increase in the particle's initial depth,
bottom undulation's amplitude, and the strength of the alongshore current.
Additionally, CBIID near the free (bottom) surface increases (decreases) with
an increase in bottom undulation's wavelength. Maximum CBIID is obtained for
long wavelength bottom topography that approximately makes $\pi/4$ angle with
the shoreline. Unlike Stokes drift, particle excursions due to
current-bathymetry interactions might not be small, hence analytical
expressions based on the small-excursion approximation could be inaccurate. We
provide an alternative $z$-bounded approximation, which leads to highly
accurate expressions for drift velocity and time period of particles especially
located near the free surface. Realistic parametric analysis reveals that in
some nearshore environments, CBIID's contribution to the net Lagrangian drift
can be as important as Stokes drift, implying that CBIID can have major
implications in cross-shelf tracer transport.
