  In this work, we obtain the deflection angle for a boosted Kerr black hole in
the weak field approximation using the optics in a curved spacetime developed
by J.L. Synge in 1960. We study the behavior of light in the presence of plasma
by considering different distributions: uniform plasma, singular isothermal
sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We
found that the dragging of the inertial system along with the boosted parameter
$\Lambda$ affect the value of the deflection angle. As an application, we
studied the magnification for both uniform and singular isothermal
distributions.
