I'm an Optician at a Naval Air Station with an Aerospace Optometrist. I can tell you that to be a Pilot, if you can't pass the depth perception test then you will not be a Pilot. There are certain exercises you can do to try to help your depth perception, but it's more along the lines of, you either have it or you don't. At most Aviation Medicine clinics, they have the Armed Forces Visual Field Test (AFVT) which tests for Visual Acuities, Phorias, and Depth Perception. The earlier link to that website is the requirement for Aviation. The test that our clinic uses is the Randot Fly Test. You have to have 40" (degrees of arc) to pass the test. From my experiences as an Optician, you either get one right and miss the other 9, or you get all of them right. It's like the color deficiency test, you either have the ability or you don't. A question I typically ask, do 3-D movies work for you? If they don't, you don't have stereo vision.
I'm new to the site, and if anyone ever has any questions about Optometry, shoot me a PM, I'll help you out.