  Recent observational data from the Event Horizon Telescope (EHT)
collaboration provide convincing realistic evidence for the existence of black
hole rotation. From a phenomenological perspective, a recently proposed stable
rotating regular (SRR) black hole circumvents the theoretical flaws of the Kerr
solution. For the purpose of obtaining observational signatures of this black
hole, we study its gravitational lensing effect. In the strong field limit, we
calculate the deflection angle of light, the radius of the photon sphere, and
other observables. The observables include the relativistic image position,
separation, magnification, and time delays between different images. Then, by
modeling M87* and Sgr A* as the SRR black hole, we compute their observables
and evaluate the deviation of the observables from the Kerr case. In the weak
field limit, we calculate the light deflection angle of M87* and Sgr A* via the
Gauss-Bonnet theorem (GBT). With the growth of deviation parameter $e$, the
gravitational lensing effect in the weak field limit intensifies monotonically,
and the gravitational lensing effect in the strong field limit changes
dramatically only at high spins. Our research may contribute to distinguish
between SRR black holes from Kerr black holes under higher-precision
astronomical observations.
