Yes. You pay the same rate as you would for using the ship's computer. I think it's .55/minute, but you can buy a package that takes it down to .33 or so. The Wifi is a lot faster, but is still slow relative to what we have on land.
And you will most likely not get reception in your cabin. There are half a dozen or so hot spots around the ship - there's a piece of paper in the computer center on Deck 4 that will tell you where.