Well, I'm not sure what "this circuit" means. I guess it's just a microcontroller or someting, in which case, a flip flop would be ideal. It should be configured as a 1-bit counter, which means a D-type F/F, for example, would connect the Q BAR or the inverse of the Q output to the D input, and your tilt switch would connect to the clock pin. However, you're going to need to "debounce" you switch, and even a normal bebounce circuit might not work well, as the tilt might "make" and "break" many times before settling. If you used a J-K FF, then I think the J & K can just be connected to VCC or ground, and it will automatically do what you want. Either way, make sure the flop is reset at power up.
I think this might a very dicey proposition, unless you can add some sort of mechaincal hysterisis to the tilt switch.