@Triplethreat117 - That looks like a timer that controls 120 VAC to a pump somewhere. The multiple fins in the top left corner that partially show up are the timings for the zone. My guess is that there is an indexing valve in the system and it moves every time the pump is turned off.
Yes, the Rachio can run this system. But, you might be better off changing out the index valve for a gang of valves in like in one of these installations:
and
Out of curiosity are you located in Florida? Indexing valves are common there.
If you have a pump that supplies water to the system, then you’ll need a pump start relay.
If the city pressure provides water and the timer is connected to the indexing valve then one just needs to connect it to the M/P port on the Rachio as described here → http://support.rachio.com/article/339-compatibility-with-indexing-valve-systems