  Recently, Cui et al. [Nature \textbf{621}, 711 (2023)] reported that the jet
nozzle of M87* exhibits a precession with a period of approximately 11 years.
This finding strongly suggests that M87* is a spinning black hole with a tilted
accretion disk. In this paper, our aim is to utilize these observations to
constrain the parameters of the black hole. Firstly, we investigate the
properties of the tilted circular orbits and the innermost stable circular
orbits. The corresponding angular momentum, energy, and Carter constant for
both prograde and retrograde orbits are calculated. We find that, compared to
equatorial circular orbits, these quantities exhibit significant differences
for fixed tilt angles. Moreover, the Carter constant takes positive values for
nonvanishing tilt angles. Notably, the presence of misalignment of the orbit
angular momentum and black hole spin leads to a precession effect in these
tilted circular orbits. We then make use of these circular orbits to model the
warp radius of the tilted accretion disk, which allows us to determine the
corresponding precession period through the motion of massive particles.
Further comparing with the observation of M87*, the relationship between the
black hole spin and the warp radius is given, through which if one of them is
tested, the other one will be effectively determined. Additionally, our study
establishes an upper bound on the warp radius of the accretion disk. These
findings demonstrate that the precession of the jet nozzle offers a promising
approach for testing the physics of strong gravitational regions near a
supermassive black holes.
