  Inner accretion disc around a black hole provides a rare, natural probe to
understand the fundamental physics of the strong gravity regime. A possible
tilt of such a disc, with respect to the black hole spin equator, is important.
This is because such a tilt affects the observed spectral and timing properties
of the disc X-ray emission via Lense-Thirring precession, which could be used
to test the theoretical predictions regarding the strong gravity. Here, we
analytically solve the steady, warped accretion disc equation of Scheurer and
Feiler (1996), and find an expression of the radial profile of the disc tilt
angle. In our exact solution, considering a prograde disc around a slowly
spinning black hole, we include the inner part of the disc, which was not done
earlier in this formalism. Such a solution is timely, as a tilted inner disc
has recently been inferred from X-ray spectral and timing features of the
accreting black hole H1743-322. Our tilt angle radial profile expression
includes observationally measurable parameters, such as black hole mass and
Kerr parameter, and the disc inner edge tilt angle $W_{\rm in}$, and hence can
be ideal to confront observations. Our solution shows that the disc tilt angle
in $10-100$ gravitational radii is a significant fraction of the disc outer
edge tilt angle, even for $W_{\rm in} = 0$. Moreover, tilt angle radial
profiles have humps in $\sim 10-1000$ gravitational radii for some sets of
parameter values, which should have implications for observed X-ray features.
