  We consider a black hole mimicker given by an exact solution of the
stationary and axially symmetric field equations in vacuum known as the
$\delta$-Kerr metric. We study its optical properties based on a ray-tracing
code for photon motion and characterize the apparent shape of the shadow of the
compact object and compare it with the Kerr black hole. For the purpose of
obtaining qualitative estimates related to the observed shadow of the
supermassive compact object in the galaxy M87 we focus on values of the
object's spin $a$ and inclination angle of observation $\theta_0$ close to the
measured values. We then apply the model to the shadow of the $\delta$-Kerr
metric to obtain onstraints on the allowed values of the deformation parameter.
We show that based uniquely on one set of observations of the shadow's boundary
it is not possible to exclude the $\delta$-Kerr solution as a viable source for
the geometry in the exterior of the compact object.
