High current power switch required?
You can use a contactor or relay for this switching application as long as the contacts are rated for the load presented by the solenoid. It is a good idea to even overrate the contacts current rating by an amount to assure that the contacts are not burned due to the inrush current as the circuit first turns on. This could be two to three times the current that the solenoid may require as normal static ON state. So that may mean you will want contacts rated for 10A or better.

Note also that a solenoid is a largely inductive load and there will be a large voltage spike created just as the relay or contactor opens to shut off the circuit. For this reason you will want to place a diode across the solenoid coil with its cathode toward the more positive voltage side of the coil. Snubber circuits are also often used for this application.

Contacts also have a DC switching voltage rating which you will want to make sure is well above the 12V that you are working with.