  The successful capture of black hole(BH) images by the Event Horizon
Telescope(EHT) has sparked a surge in research on strong gravitational lensing,
providing new methods for studying behavior near the event horizon of BHs. For
the short-hair that has significant effects only near the BH event horizon,
studying its strong gravitational lensing effects helps to understand the
nature of this hair. This paper explores the behaviors of the rotating
short-hairy BH in strong gravitational lensing. Simulations show that the
short-hair parameter results in a smaller event horizon radius, photon sphere,
and impact parameter compared to the Kerr BH. Moreover, the lensing
coefficients $ \bar{a} $ and $ \bar{b} $ show opposite trends due to the
short-hair parameter $ Q_m $, with the former increasing and the latter
decreasing. It is worth mentioning that in certain cases, the short-hair
parameter can make $ \bar{b} $ slightly higher than that of the Kerr BH. The
deflection angle $ \alpha_D $ decreases with an increasing impact parameter and
diverges at $ u_m $, with the divergent impact parameter of rotating
short-hairy BH being smaller than that of the Kerr BH. In the context of
$M87^*$ and $Sgr A^*$ BHs, their Einstein rings, relativistic images, and time
delays differ significantly from those of the Kerr BH. Although current
equipment cannot yet distinguish these differences, future high-precision
instruments are expected to achieve this goal, thereby differentiating rotating
short-hairy BH from the Kerr BH, exploring the nature of the short-hair, and
testing the no-hair theorem of BH. This provides a new perspective for
understanding the extreme physical environments of BHs and offers necessary
references for future observational and theoretical research.
