Of course you can bring it on the plane and through security in your carry on bag, hundreds of thousands if not millions of travelers do everyday. You are not allowed to use the phone unless you have an "airplane mode" which prevents any wireless transmission and phone calls. The flight attendants or the captain will usually announce when it's okay to turn on your phone, otherwise keep it off until the plane reaches the gate although some airlines now permit you to use your phone after the plane has landed and taxiing to the gate.
You can bring it in your carry-on. You can (and may) use it on the plane while sitting waiting to leave the gate. They will tell you to turn everything off when they close the door. Then you may not use it until you have landed and the plane has turned off of the runway. But as to the can/may issue, you might or might not be able to use it inflight. But you may not.