You can but it will require modifications.
1. OpenSprinkler Pi can run on 12V DC. Make sure that when you connect the DC wires to the terminal block, the pin closer to the power switch is ground, so the negative wire should go to that pin. Don’t worry if you accidentally reversed the polarity — there is a rectifier diode that protects the circuit.
2. The more tricky part is the solenoid drivers — because OpenSprinkler Pi is designed to work with AC valves, it uses triacs (ac transistors) to control valves. If you directly plug in DC valves, you will find that they can only be turned on, and once on they can never be turned off. That’s because of the way triacs work. So you will need to either replace the triacs by transistors or MOSFETs, in order to directly interface with DC valves, or you can also use an external relay board. This blog post provides some details about using relay board:
http://rayshobby.net/?p=4717