The short answer: maybe.
1. Assuming you are just visiting for a holiday ask your cell phone provider for their rates and also, VERY important, ask them to remove any restrictions on using your phone overseas. This is my personal least favourite way because it usually is so damn expensive.
2. Ask yourself.. do you really need the phone part of your cellphone? ALL cell phones can connect to ANY WiFi in any cafe or hotel anywhere in the world. Via WiFi you can look up maps (take a screenshot to save the map when you are not in a WiFi area), retrieve your email, post Facebook updates; in fact you can do anything but make a phone call. But wait, you can use WiFi based Skype or LINE to make a phone call.. for free! If this is the case any cellphone, iPod or tablet will also suffice.
3. If your phone is UNLOCKED and is a GSM type of phone then you can make a call and connect to the internet via a cell tower data connection. Before you leave your home country, ask your cell phone provider to UNLOCK your cellphone, you then take the phone to a provider at your destination. They will sell you a “SIM” or “chip” for your phone. Your current SIM is removed and replaced with the new SIM. Keep the current SIM in a safe place for your return home. Assuming you will return one day :). The next step has many variables.. but basically you need to add money on to the new SIM in order to use the phone. This is my favourite way to use my cell phone.. it is usually a much, much cheaper method and I can connect to maps, email, Facebook while I am anywhere with a cell date data connection.
If your phone is not unlocked or if your phone is not a GSM cellphone then your options are limited. Check before you leave your home country. A fourth option is to simply BUY a phone at your destination.. these cheap.. cheaply made.. cheap to buy cellphones come with call time already available, but these cheap phones can only make calls, but sometimes may include free Facebook or LINE communication.