Yes. All Carnival Cruise Line ships offer Internet connectivity and have on board internet cafes. You will have to pay for the service though, generally on a by-minute basis. Rates can range anywhere from .35 per minute to $1.25 per minute. Rates will vary based on a number of things including the day of your trip you purchase your package. There will be deals and packages offered on port days and embarkation days. Your rate per minute will also go down when you purchase packages offering more minutes. To beat the high prices, try checking into an Internet cafe in a port.
For more info, see Carnival Victory Cruise Ship