In no way is this a draw. It is actually a very simple theoretical win for Black. The White King is stalemated. So 1... Rb1+ foreces the exchange of rooks. Since white must give up control of the key square h2, Black wins easily
1... Rb1+ 2. Rf2 Rxf2+ 3. Kxf2 Kh2 and White cannot prevent the pawn promoting.
no rook to b1 rto f1 rxr kxr kh2 and advance with the pawn
I thought you had switched which side was to move when I first read your post. With White to move this is a Philidor TYPE position. 1. Rf1 g2 2. Rf3+ Kg4 3. Rf6=
The Philidor is more like this, but you can see how they are related.
The issue being that Black's rook cannot leave the second rank because it must secure the pawn and the black king has no shelter from the checks. To win, using Lucena for example, Black would have to shelter his king using the pawn and/or the rook.
Matalino, I chose to demonstrate the checks from the side because it relates better to the position the poster was asking about. Attempting to check from behind in Fast_Thinker's position would lead to a loss for White, not a draw. This is why I used terms like "Philidor TYPE" position and "similar." While your explanation of the Philidor is more in-depth and more technically correct, it does not relate to the poster's question as accurately.
Definitely NOT a draw. Look:
Wrong side to move oopps.