Is it possible to make mouse movement act like an FPS?

I feel like something that prevents me from doing well in RTS games is the fact that the cursor can move in relation to the screen. I primarily play FPS-genre games, and would strongly prefer that the cursor be fixed to the center of the screen, moving the world as I move the mouse, just like an FPS.

As the biggest RTS being played by my friends right now is Starcraft 2, is there a way to make Starcraft 2 act like middle-mouse is always down, but still respond to left/right-mouse for clicking, drag-selecting, right-clicking, etc.?