  In this paper, we introduce a method for calculating the deflection angle in
the weak-field approximation, applicable to both null and timelike rays. By
combining the trajectory equation $\mathcal{Z}(u)=(du/d\phi)^2$ and the
`straight line' $u(\varphi)={\sin\varphi}/b$, we introduce a new function
$\Phi(\varphi)$. The deflection angle can then be expressed as
$\delta=\Phi(0)+\Phi(\pi)-\pi$, which directly depends on the impact parameter
rather than the closest approach distance. This method offers a convenient and
straightforward approach to calculations, avoiding the complexities of
integration or iterative procedures. As an illustrative application, we compute
the deflection angle for charged particle in the Kerr-Newman spacetime.
