One of the GPIO (General Purpose I/O) pins of the Pi can be used to "send an extend signal" to the solenoid circuitry.
That signal probably can't be used by itself because of current requirements of the solenoid and other interesting things that happen when the signal is turned off and the solenoid stops getting powered on. For THAT you'll need some sort of interface circuitry from signal to solenoid, typically involving buffer/power elements as well as, minimally, a diode to protect things when the solenoid turns off.
But, yes, the Pi for sure can signal (indirectly) to a solenoid to activate - not a problem at all.
Your best bet is to Google search for various things like "turn on solenoid digital", etc - you figure out what the various things are. You'll see that the interfacing circuitry - even if you use discrete components like transistors instead of IC chips, is pretty simple.
I did a quickie search (not well thought out) and found, for example, http://mbed.org/users/4180_1/notebook/relays1/
which looks like an info-full page.