  The nonminimal coupling of the nonzero vacuum expectation value of the
self-interacting antisymmetric Kalb-Ramond field with gravity leads to a
power-law hairy black hole having a parameter $s$, which encompasses the
Reissner$-$Nordstrom black hole ($s=1$). We obtain the axially symmetric
counterpart of this hairy solution, namely, the rotating Kalb-Ramond black
hole, which encompasses, as special cases, Kerr ($s=0$) and Kerr-Newman ($s=1$)
black holes. Interestingly, for a set of parameters ($M, a$, and $\Gamma$),
there exists an extremal value of the Kalb-Ramond parameter ($s=s_{e}$), which
corresponds to an extremal black hole with degenerate horizons, while for
$s<s_{e}$, it describes a nonextremal black hole with Cauchy and event
horizons, and no black hole for $s>s_{e}$. We find that the extremal value
$s_e$ is also influenced by these parameters. The black hole shadow size
decreases monotonically and the shape gets more distorted with an increasing
$s$; in turn, shadows of rotating Kalb-Ramond black holes are smaller and more
distorted than the corresponding Kerr black hole shadows. We investigate the
effect of the Kalb-Ramond field on the rotating black hole spacetime geometry
and analytically deduced corrections to the light deflection angle from the
Kerr and Schwarzschild black hole values. The deflection angle for Sgr A* and
the shadow caused by the supermassive black hole M87* are included and compared
with analogous results of Kerr black holes. The inferred circularity deviation
$\Delta C\leq 0.10$ for the M87* black hole merely constrains the Kalb-Ramond
field parameter, whereas shadow angular diameter $\theta_d=42\pm 3\, \mu$as,
within the $1\sigma$ region, places bounds $\Gamma\leq 0.09205$ for $s=1$ and
$\Gamma\leq 0.02178$ for $s=3$.
