  We propose a model of a twisted accretion disc around a Kerr black hole
interacting with a secondary black hole of a smaller mass on an inclined
eccentric orbit. We use parameters of the system, which may be appropriate for
the so-called 'precessing massive' model of OJ 287. We calculate expressions
for torque exerted on the disc by the secondary and a contribution of the
secondary to the apsidal precession of disc elements by a double averaging
procedure over the periods of the secondary and the disc elements. These
expressions are used at all scales of interest, including the ones inside the
binary orbit. We calculate numerically the evolution of the disc tilt and twist
assuming a flat initial configuration. We consider the disc aspect ratio
$h/r=10^{-3}$, a rather large viscosity parameter $\alpha=0.1$ and several
values of the primary rotational parameter, $\chi$. We find that, after a few
periods of Lense-Thirring precession of the orbit, the disc relaxes to a
quasi-stationary configuration in the precessing frame with a non-trivial
distribution of the disc inclination angle, $\beta$, over the radial scale. We
propose an analytic model for this configuration. We show that the presence of
the twisted disc leads to multiple crossings of the disc by the secondary per
one orbital period, with time periods between the crossings being different
from the flat disc model. Our results should be taken into account in the
modelling of OJ 287. They can also be applied to similar sources.
