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We study the light deflection effect and the relativistic periastron and frame-dragging precessions for a rotating black hole localized on the brane in the Randall-Sundrum braneworld scenario. Focusing on a light ray, which passes through the field of the black hole in its equatorial plane, we first calculate the deflection angle in the weak field limit. We obtain an analytical formula, involving the related perturbative parameters of the field up to the second order. We then proceed with the numerical calculation of the deflection angle in the strong field limit, when the light ray passes at the closest distance of approach to the limiting photon orbit. We show that the deflection angles for the light ray, winding maximally rotating Kerr and braneworld black holes in the same direction as their rotation, become essentially indistinguishable from each other for a specific value of the negative tidal charge. The same feature occurs in the relativistic precession frequencies at characteristic radii, for which the radial epicyclic frequency of the test particle motion attains its highest value. Thus, the crucial role in a possible identification of the maximally rotating Kerr and braneworld black holes would play their angular momentum, which in the latter case breaches the Kerr bound in general relativity.