Can I own land without having a city nearby?
Solution 1:
There is a way, but it likely involves too much work.
To answer your question directly - which assumes you settling near that area is not an option - there are two ways to do this:
1) Expand your borders:
Eventually, your borders will keep growing even past the 3 workable tiles. I believe the maximum is 5, so if it's close - you'll eventually get it.
In addition, even if it's 20 spaces away, you can still get it. To do this, you'll need a bunch of Great Generals. These guys can simulate what was known in the past as a culture bomb. Place them on the border of where you want to expand, and consume them to create a citadel; this will expand your border 1 tile in all directions (it will even replace other civilizations borders with yours!). With enough Great Generals, you can get anywhere you want (and your borders can look quite odd - too!)
2) Gifting 'glitch'
I'm not sure if this is a glitch or not, but this also involves great generals. To do this, annex a city with tiles you want within its borders. Then, consume a great general over the tiles you want to keep. When your city stops revolting, trade it to a civilization - they'll get the city, and all the unhapiness - while you keep the citadel tile and its surroundings.
Often this results in you having small, uncontected patches of land all over the place.
Solution 2:
Depending on the location relative to your current territory, it's possible that your borders will eventually envelop this island. It takes progressively more culture per hex annexed into your borders, though, and your borders are unlikely to take tiles on the other side of another player's territory. If it's very close and you've got time to wait, chances are you'll eventually "own" the island.
You can found a city on this island, and then the tile the city is on and the surrounding area will be considered yours. However, the benefits of this aren't really all that awesome if the area is not desirable. The only benefits I can think of is any "in your territory" bonuses from wonders or social policies, and the possibility of airlifting units in and out if you've researched the relevant technologies and built an airport.
You can make a "staging area" there if you wish, even if it isn't in your territory. Having a unit in a hex will prevent other units from being there, so you can just order your units to stop over at the island on their way to the war and get most of the benefits of a staging area without actually building anything there.