This happens due to the relative velocity. The relative velocity of rain with respect to car is the difference in the velocities of the rain and the car. \[\text{i.e.}\;\; v_{\text{rel}} = v_{\text{rain}}-v_{\text{car}}\] [From Triangle Law of Vector Addition]
It means that the magnitude as well as direction of the velocity of rain as observed by a person inside the car is different. This gives the displacement also different from the original, both in terms of magnitude and direction. So, the person inside the car sees rain drops coming in direction AC rather than AB.
Let $R$ be the resultant which makes an angle $\theta$ with the vertical. Then, \[R=v_{\text{rain}}^2+v_{\text{car}}^2\] and, \[\tan\theta=\frac{v_{\text{car}}}{v_{\text{rain}}}\] \[\theta = \tan^{-1}\left(\frac{v_{\text{car}}}{v_{\text{rain}}}\right)\]
Therefore, the rain strikes the front windscreen by making an angle $\theta$ with the vertical so the windscreen gets wet.
