You used to be able to order rigid forks with any length of steerer tube; I don't know if that is still possible. Call your LBS to see. Just remove the old fork and measure the length of the steerer from the top of the crown to the top of the tube and order the same thing.

It is definitely easy, however, to get a rigid fork with a threadless steerer, a threadless headset, and a threadless stem.

You will also need to get a new cable hanger, eigher fork-crown-mounted or headset-mounted, as your front brake cable is currently on your fork.

Not only is this possible, but an excellent idea! A rigid fork will make your bike lighter, easier to maintain, and less likely to be stolen.

(edit: provided it is a 1-1/8" steerer on the existing fork... if it is 1" it may be hard to find a replacement.)