  We analytically investigate the shadows cast by rotating black holes in the
asymptotically safe gravity (ASG) by deriving complete null geodesics and
observables using the Hamilton-Jacobi equation and Carter separable method. It
turns out that the apparent shape and size of the shadow depend on the ASG
parameters ($\zeta, \gamma$) in addition to other black hole parameters ($M,
a$). The size of black hole shadows monotonically decreases and shadows get
more distorted with increasing values of ASG parameters when compared with the
Kerr black hole shadows. In turn, we use shadow observables to estimate black
hole spin and ASG parameters. Noteworthy, we find that the deflection angle of
the light has been modified by ASG parameters to generalize the Kerr deflection
angle, and the corrections in the deflection angle are of $\mathcal{O}(\mu$as).
In the vanishing limits of ASG parameters, our results smoothly reduced to the
Kerr black holes. The inferred circularity deviation $\Delta C\leq 0.10$ for
the M87* black hole shadow merely constrains the ASG parameter $\zeta$,
however, shadow angular diameter $\theta_d=42\pm 3\, \mu$as, within the
$1\sigma$ region, places bounds $\zeta\leq 0.1324$ for $\gamma=0.10$.
