Answer
Tilted forward.
Work Step by Step
Let $V_{rp}$ be the velocity of the rain relative to the person.
Let $V_{rg}$ be the velocity of the rain relative to the ground.
Let $V_{gp}$ be the velocity of the ground relative to the person.
So, $V_{rg}$ is a vertical vector pointing down and $V_{gp}$ is a horizontal vector pointing backwards (if the person is running forward, he watches the ground moving backwards).
But, $V_{rp}=V_{rg}+V_{gp}$. (see the figure).
So, the person should hold the umbella in the opposite direction of $V_{rp}$, that is, tilted forward.
