Yes you can! There are few options should you wish to use a cell phone in Peru.
You can rent one on arrival in Cusco or Lima airport. There are rental places in both airports, and there are often several people at the arrivals gate selling rentals.
You can bring your own cell phone, but make sure it is a tri-band phone that can be used in other countries, then when you are here you can purchase a chip or SIM card from one of the many cell phone shops around.
Lastly you can just buy a complete cell phone. I recently bought a cell phone from Claro for 59 Soles ($22) with 20 minutes of free talk time to other Claro phones. Top up cards can be purchased at all Claro stores, and the staff will even top up the phone for you.
I personally would purchase a phone as this is probably the most flexible and cheapest method.