Yeah you can add an international data plan:
- $24.99/month: 20 MB Data Global Add-On gives you 20 MB of usage within over 90 countries
- $59.99/month: 50 MB Data Global Add-On gives you 50 MB of usage within over 90 countries
- $119.99/month: 100 MB Data Global Add-On gives you 100 MB of usage within over 90 countries
- $199.99/month: 200 MB Data Global Add-On gives you 200 MB of usage within over 90 countries
This is is on top of your regular plan; and any usual browsing, you're looking at 25MB, so unless you are only going to using the network no more than once or twice, you're pretty much stuck with paying for the 100MB or 200MB plan.
FYI, if you don't get a plan, then you're looking at thousands out the window by the time you get back.
Finally the plans that are labeled unlimited [or 5GB] (for international data) you need to sign a 1-year contract to keep it on or they will charge ETF of $175.
More info on plans
here.
My advice is to just unlock your phone, get a local SIM card and use data pay-per-use which will probably be cheaper not to mention you'll be able to make calls.
Of course the best solution is to not use the iPhone since it's a data hog.
To answer you original question:
You will need to pay extra to roam internationally.
Have a good trip.